Hi everyone, Joe for jaspyscasebrakes.com coming at you with a quick little filler break. We'll sell a pack break, we're gonna do the break first and then at the end we'll re-randomize your names in a different dice roll and give away some national treasures football spots. Big thanks to this gang right here for getting into it, appreciate it. All 32 teams are in. Let's roll it. Randomize names and teams, snake eyes, two times, nice and easy, one and two. Two times for the teams, one and two. Browns down to Falcons and then again a completely different dice roll for the giveaway part. We're gonna do one more of these packs a little bit later tonight that'll unlock the NT break. Here's the first half of the list here, Josh with the chargers, second half of the list right here, Josh with the bangles. Could there be something interesting in here? It has happened before, the whole point of this really is not what's in this break, it's mostly the spots that were given away, but every once in a while you'll get something nice like a silver rookie or something like that, it pops out of here. Green Cortland Sutton, AJ Eponessa, alright nothing too crazy there, red, white and Sam Hubbard, maybe his teammate, Alan Lazard, that's not bad. Lyons, Joshua Edelitz, alright. Now let's re-randomize those names and it's gonna be the top six after seven. Good luck, one, two, three, four, five, six and seven in final time. And no worries Hollywood, always glad to help, alright from seven on down, not any help to people from seven to thirty two though, sad times. But happy time, I'm a big help for the top six, Josh, JC, Fuad, Matthew, Joshua and Sean, congrats to the top six here in that NT break. Coming up a little bit later tonight, jaskyscasewrakes.com.


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Good afternoon everyone and welcome. This is Melissa Armo with the stock swishing. I'm here to review the spy And I wanted to do this today because interestingly enough the market gap down and when I first viewed this this morning I thought geez you know this actually kind of looks like we might drop today like it's possibly bearish as it turns out We didn't fall Then when I noticed the way the market traded in the morning I said wait a minute this might actually hold and flip and if it does it'll be very strong And that was accurate. I went back then I rated the gap Which I don't normally rate the gap in the market, but you can rate the spy the QQQs You can read any ETF with my golden gap system as long as it's gapping. So I rated this it rated 19 points 20 is the cutoff for something to work on the direction of the gap for my 26 point system But this really did rate right on the cusp and 19 is close Sometimes 19 point rated gaps do work. It's a 50 50 So this didn't today and it's very interesting because this is an extreme sign of strength to happen to rally the way That we did all day here today We pretty much power trends it all day with the gap down in the market So I'm gonna first look at the daily chart then I'll look at the one minute Big move here for the spy today. Okay? Nice big beautiful move. Low is 231 61 high is 233 82. Where are we? I mean we held and gapped down in a baby support and This is a real sign of bullishness in the market. So no matter what we do in here I think we rally tomorrow I think if we gap down a little bit will rally if we gap neutral will rally if we get up will rally This looks very strong. I'd be shocked if we gap down anything significant tomorrow in the market after today's rally It could happen. I won't know to the morning, but this looks very bullish So all signs point to go higher for the market Which means that we barely even came in hardly at all. Let me just look here at the Spy So what happened here was dropped rallied we went green Set up fell Bounced held held the low and then took off like a banshee So this move happened in the morning in the period didn't fall didn't break But I remember watching this in here, and I remember thinking gosh That's odd because I really felt that the way or the gap was and look this morning that if we were gonna drop and break We'd fall off a cliff immediately five minutes into the open and we didn't do it We did not do it. So a lot of strength here in the market Lot of strength. I mean to to fail on a gap down here to go lower Rally all day in power trend hold Rally up over the 50 premium average. I mean thing after thing after a thing after a thing The rating I mean all of this tells me that the market is going to lift Tomorrow's Tuesday Wednesday Thursday Friday Finishing out the calendar month of March. We'll see where the market goes I'm not saying we make a new high before the end of this week There's only four days left But I'm saying if buying wants to come in and just go go go go go There's a possibility we could once we get over this level here that red bar in the gap up that failed and ran down all day on this Day back last week. I mean anything's possible So previous high was 240 32 So nice bullish market today email me with at Melissa at the stocks wish calm if you have any questions And if you'd like more information about the next golden gap course to learn my method It's April 8th and 9th. Good luck everyone this week. Be very careful The bull stepped up to the plate today. The bears were not in control. I never thought that they were but there are some people that are short this market and They're gonna get run over. Good luck everyone. Have a good week


It's a pleasure to be here. So I'll talk about, I think, the main theorem is already described in the abstract, so I'll try to start by giving a little bit of some related history. The problem is to cover almost all the integers up to some point using as few binary quadratic forms as we can. And the study of binary quadratic forms, of course, goes back a long way to Verma. And we know what integers are sums of two squares. So they are all integers which are divisible only by primes that are 1 mod 4. Or you could have primes that are 3 mod 4 so long as they appear to an even exponent. So you can count several things. You can either count with the number of representations the number of representations if I denote by Rn. We could count the total number of integers up to some point n, counted with this multiplicity Rn. That's just counting the number of lattice points inside a circle. And this is a circle problem. We know it's approximately the area of the circle plus some remainder term, which is still open what the best error term should be. Or we could count just the number of integers up to n that are represented as sums of two squares. And this also is a classical problem going back to Landau. And we know that the number of integers that are represented by this binary quadratic form is about n over root log n. And Landau's result was generalized by Bernays shortly afterwards. So the same proof goes through for essentially any binary quadratic form, let's say positive definite. So something of the form ax squared plus bxy plus cy squared. And then the relevant quantity here would be the discriminant b squared minus 4ac. And the discriminant is negative in this case if we think of positive definite binary quadratic forms. There are many other interesting results about binary quadratic forms. Let me just say a couple of them from more recent history and which are also relevant to the theme of this talk. I think a very beautiful result is due to Blomer. I think this is part of his PhD thesis from around 2005. And Blomer showed that if you look at the number of integers up to n that are sums of two square full numbers. So sums of two squares are obviously sums of two square full numbers. A square full number is one where every prime factor appears to exponent at least three, at least two. But what he showed was that there are many more integers that are sums of two square full numbers than sums of two squares. And the exponent on log n here instead of half in Landau's theorem is actually something like 0.2, one minus two to the minus one third. And what Blomer did here was to count a square full number can be written as a squared times b cubed. So what you're counting here is representations by this family of binary quadratic forms, a cubed x squared plus b cubed y squared as you vary A and B in certain ranges. There are more precise versions of this by Blomer and Granville. I think they even get the right power of maybe, maybe they refine this up to powers of log log. They also study related problems like looking at moments of the representation function of n by some fixed binary quadratic form and then studying this both in regard to, you know, how you can vary beta and also with regard to uniformity in the format. And these kinds of results have also found applications in other areas like work of Borgen and Fuchs to numbers that appear in Apollonian packings as curvatures of circles in Apollonian packings. Okay, so that's a little bit of review of related results. I want to now get to the problem at hand, which is if you take a family of binary quadratic forms, x squared, let's just say x squared plus d y squared and d goes up to some parameter delta, then the question is how large should delta be so that this family of binary quadratic forms represents almost all the numbers up to n or you could also ask how large must delta be so that you get a proportion of the integers up to n. Now, each binary quadratic form by the result of Landau or Bernays represents about n over root log n numbers. So you must clearly have delta being at least some constant times root log n if you're going to represent a positive proportion of numbers. But the set of numbers that are represented by two different quadratic forms may have dependencies and so therefore maybe this is not the right answer and we have to study how two of these sets intersect with each other if we want to determine exactly what delta is. So this seems like a fairly natural problem but it seems to have been considered only quite recently where so work paper of Brandon Hansen and Bob Vaughn from 2020 where they showed that if delta is a little bit larger than log n so maybe log n times some power of log log n log log n to the fourth, then you can represent almost all numbers up to n by this family of binary quadratic forms and they had a refinement that if you only want a positive proportion then you can save some powers of log log. This is largely as an application of the circle method computing a second moment. There's a student of Blohmer, I think part of his master's thesis, Dell, who showed that a refinement of this result of Hansen and Vaughn, he showed that you could deal with prime values of D rather than just all D up to delta. So the set of binary quadratic forms the considers has size about log n rather than log n times log log n but you still have to go up to the same log n times log log n in order to represent almost all numbers. So the result that I want to give some indication of today maybe once I state the theorem to the experts it'll be clear what the proof is is a result with Ben Green which we are still writing up which determines the threshold for when you can represent almost all numbers or when you can represent any even a proportion of numbers. So if you have delta which is approximately log n to the log two and then there are smaller fluctuations around it. So some parameter two to the alpha times square root log log n then at this stopping point the proportion of integers up to n that you would represent by this family of binary quadratic forms is the Gaussian integral. So as alpha goes off to infinity you would get almost all numbers and as alpha goes to minus infinity you would get 0% of the numbers. So in other words just to give a cruder corollary if you stop at log n to the log two minus epsilon then you've not represented many of the numbers up to n and if you stop at log n to the log two plus epsilon then you've represented almost all the numbers up to n. So where does this threshold come in? It comes from the typical structure of an integer. So most integers up to n have about log log n prime factors and it doesn't matter whether you compute count the prime factors with multiplicity or without multiplicity it doesn't matter whether you have little omega or capital omega and we can be more precise than that we have the result of Erdisch-Katz which says that you have a Gaussian law both of these parameters behave like a Gaussian with mean log log n and variance log log n. So that's where the Gaussian integral in the theorem comes in. And then even more precise version of this I've given it in a special case you can actually take any k uniformly in a wide range but let's say if we focus on the range where are typical numbers so k is close to log log n and a little bit bigger than the standard deviation but not too much bigger then you can give an asymptotic formula for the number of integers up to n that have exactly k prime factors. And that has this feature if k is one, this is the prime number theorem it's not in this range but you can see that that's the prime number theorem and it has, it's actually, you know now that one states it this way the Erdisch-Katz theorem is always stated as being a Gaussian with a certain mean and a certain variance but you could see from the way I've stated it here it's much more reasonable to think of the distribution as being a Poisson with parameter log log n this is a Poisson distribution with parameter log log n but a Poisson with large parameter approximates a Gaussian with that parameter and the same standard variance that follows just by Sterling's formula if you put in Sterling's formula for approximating gamma of k, of gamma of k or k minus one factorial then you see that the number of integers with k prime factors has this kind of Gaussian behavior so the result that Ben and I prove is actually even a little bit more precise I will state it again for just this range of typical values of integers but in fact the proof should work for k in wide ranges not just of the typical size so what the result says is that if you consider the subset of integers with exactly k prime factors then if delta is below the threshold if it's smaller than 2 to the k by let's say k to the fourth then 0% of the integers in the set are represented by one of these binary quadratic forms so we call this the upper bound result and upper bound means that we give an upper bound for the number of integers that are represented by this family of quadratic forms correspondingly if you go a little bit past the threshold if you go some power of k away from 2 to the k then the number of integers that are not represented by this family is actually small so here we save a tiny bit over the trivial bound so we save only a log log log n but it goes to zero and so this means that once you go beyond the threshold of 2 to the k then almost all numbers with exactly k prime factors are represented by this family of binary quadratic forms now from this the main result that I stated in the stated before and stated in the abstract follows because if you think of k as being log log n plus alpha times square root of log log n then the Erdisch-Kass theorem will tell you what the proportion of integers that are represented up to n is and you would get the Gaussian integral from that so that's a description of the main results and if there are any questions I can answer these. Okay, so let me try to first describe why this threshold of 2 to the k arises and then give some sketch of the proof so there's a well-known link between binary quadratic forms and imaginary quadratic fields which I would say goes back to Gauss but I have no real knowledge of history so probably that's some made up history so to recap this let's think of discriminants of the binary quadratic form so this is some negative integers since we are working with positive definite forms and the discriminant is always zero or one more four since it's b squared minus four ac and we will restrict attention to fundamental discriminants so fundamental discriminant means that you're not do so by the square of some number except for four if you have to have a four in it and it's also discriminants of the imaginary quadratic fields and we know that there's a relation between the binary quadratic forms of discriminant t and ideal classes in the imaginary quadratic field q square root of d so the number of binary quadratic forms of this discriminant is the same class number as the ideal class number of the field and when I say number of binary quadratic forms I mean up to equivalence by transformations in SL2Z the class number is about square root of d it's square root of the discriminant times l1 chi d this is true once the apart from d being minus three or minus four so most of the time it's gonna be true and this character chi d is the principle is the quadratic character to the modulus d and what it means to be a fundamental discriminant is the same as saying that this character is primitive so this is the chronicle symbol here now what we know is that the total number of representations of an integer m by all binary quadratic forms of this discriminant is the same as the well I think there might be a factor of two but it's essentially the same as the number of ideals in K of norm m the two comes from the fact that your imaginary quadratic field is going to have just two units one and minus one now the number of ideals in K of norm m that's these are the coefficients of the delicate data function with just factors as the product of data of s and ls chi d so that's just the convolution of the function that takes the value one all the time with the quadratic character chi d so this counts the total number of representations by all binary quadratic forms of discriminant d but in our family what we are really interested in is the principle form x squared plus dy squared if the discriminant is a multiple of four or x squared plus xy plus one plus the size of d over four if the discriminant is one multiple and the principle quadratic form corresponds to counting representations of m to counting ideals of norm m that are principle ideals in K so okay this works when d is not three multiple so this would be the principle form but when d is three multiple you have a slightly different quadratic form but the values of this quadratic form are related to the values of the diagonal form that we are interested in by just this identity so we are counting if you have y being even then a representation here will give rise to a representation by the form that's of interest to us so here's a heuristic idea of why two to the K is the right threshold for this problem take a number n that has K prime factors and let's just assume that n is square free for simplicity so you have prime p1 to pK and suppose I want to represent n by some binary quadratic form of discriminant d that's the same as saying that all these primes p1 to pK are split in my quadratic field q square root of d which means that all of these Legendre symbols are one and the prime pI splits us as the product of two prime ideals pI and pI bar now this splitting condition is you know if I give you a value of d then it happens with equal probability for each prime p the chance that this happens is one half so if I want all of these guys to be one then the probability that all of these K things happen is about two to the minus K so if I give you a number m the chance of finding a discriminant d for which all of these prime factors are quadratic residues have chi d of pI being one is two to the minus K which means that if I count if I run over all the discriminants up to size delta then even if I add all of these up I should be at least a little bit larger than two to the K in order for them to count a substantial proportion of numbers so that means that if I go up to just two to the K over K to the four then I'm unlikely to find a discriminant d which counts I'm unlikely to exhaust many, many numbers up to m and this can be made precise very easily and I'll show that in a bit now the lower bound of the part of the heuristic that with these many binary quadratic forms that I can represent almost all integers that's the hard part of the proof but a heuristic reason for why you should believe that is that if I am at this threshold I have gone substantially beyond two to the K so it's quite likely that I will find at least some discriminant for which all of these primes are quadratic residues now suppose I found such a d then each one of these primes factors as the product of two prime ideals which means that if I take n which is a product of p1 to pK there are many, many factorizations of n as a product of two ideals of norm n so there are two to the K such factorizations now the discriminant is of size square root of d so the number of ideal classes the class number is really of size square root of the discriminant which is about size square root of two to the K so in other words the number of ideal classes is much smaller than the number of factorizations of n so if you believe in some kind of equidistribution you might believe that every ideal class there will be some factorization or many, many factorizations that will lie in every possible ideal class so in particular there are lots of factorizations of n and it's likely that some of these ns will actually correspond to principal ideals because the class number is small so therefore you should believe that as soon as n is represented by some binary quadratic form of discriminant d it's in fact represented by the principal binary quadratic form of discriminant d and therefore this threshold should be enough so that's the heuristic motivation for the proof and now for the remainder of the talk I'll give you some idea of what actually is involved in proving it let me start with the upper bound part which is basically the same proof that I already discussed so here I'm just going to count the total number of representations of an integer by all binary quadratic forms of this discriminant d and there is no loss in doing so because we expect that if you are represented by a binary quadratic form of discriminant d then you are represented by basically every form as well now this total number we can easily count using the hyperbola method if I don't worry about error terms I don't even have to use hyperbola method I just interchange sums this sum let's just pretend this n over l and then what I have is just n times l one chi d now if I consider numbers with k prime factors and you're represented by x squared plus dy squared then this representation number must just be the total number of divisors of n and let me just pretend that n is square free so the total number of divisors of n is just two to the number of prime factors two to the k this is not strictly speaking correct since I'm writing down capital omega here but it's more or less fine so that means that the number of integers up to n that are represented by this binary quadratic form is utmost since everything here is positive is utmost the total number n times l one chi d divided by two to the k if I sum this overall d going up to delta then just taking the union bound I can see that the number of integers that are represented by some binary quadratic some form x squared plus dy squared with d less than delta is no more than the sum of l one chi d up to this range times n over two to the k and l one chi d is really a very tame object it's just of constant size most of the time and therefore that just gives me n times delta over two to the k which means that if I go up to a small up to a little bit less than two to the k then very few of the numbers up to m are going to be represented so this proves that if I stop a little bit less than sorry that if I go up to log n to the log two times two to the alpha root log log n then I get less than the Gaussian integral phi of alpha as a proportion of integers that are represented now the lower bound is a bit more involved and it's really an application of the second moment method so for simplicity, let me just restrict attention to n being odd you have to do a little bit of casework to cover n being odd and then to cover n being two mod eight and then to cover n being six mod eight in with different discriminants in different residue classes so let me just restrict give you the idea of the proof in the case that n is odd and I'm going to cover them only using discriminants that are seven mod eight and discriminants going up to delta and if d is seven mod eight then the fundamental discriminant associated to this binary quadratic form is actually just negative d itself and the principle form is this x squared plus xy plus d plus one over four y squared so what we are interested in is counting the number of principle ideals of norm n in this imaginary quadratic field which really corresponds to representations by this principle binary quadratic form but here's where this condition that d is seven mod eight allows me to finish this issue if d is seven mod eight d plus one over four is even and so if n is odd you can also deduce that y must be even here and then a representation by this binary quadratic form already gives me a representation by the form that I want x squared plus d y squared so there's just a little parity check that you can make to show that in this case we can just get representations by x squared plus d y squared which would correspond to an order in q square root of d rather than just the full ring of integers so now a natural idea to try is to compare two moments let's count here the sum of all these representation numbers as d varies and compare the first moment with the second moment now if you do that then well this quantity obviously is zero if n is not represented by one of these binary quadratic forms and it's non-zero if it is represented by some binary quadratic form so therefore if you use Cauchy Schwartz you get a lower bound for the number of integers that are represented it's just at least as large as the first moment squared divided by the second moment this will kind of work to show that you can get a positive proportion of numbers but if we want the more refined result that we want to get almost all numbers with this given number of prime factors the constants don't work out and the reason is that the representations by these binary quadratic forms are not quite independent so if you have two different moduli d and d prime and let's say one of them is one more three and the other is two more three then you're not going to represent any integer n that's a multiple of three by both of these binary quadratic forms because for one of these three will be a quadratic residue and for the other three will not be a quadratic residue so there will be fluctuations so when we compare the sum this will not if the two moments are going to match then these sums must be more or less flat and what I'm saying here is that they will not be more or less flat if there are these dependencies another reason for it is that if I take even discriminants that lie in the same progression and if I look at integers n that are multiples of three now it's kind of more likely that you will be represented by both of them because three already will be a quadratic residue module of both of them so the multiples of three will be over represented and then other non-multiples of three will be underrepresented and once again this will cause fluctuations in the two moments and the two moments will not match up as far as constants go so to refine this what we are going to do is a modified second moment method where we are going to fix the in progressions modulo all the small primes and then also take the small prime factors of n into account so here's an idea of the refined version of the proof I have a parameter w which is going to go to infinity extremely slowly it can go arbitrarily slowly to infinity but if you like you can think of it just as log log log n so the discriminants d already go up to log n so even if you take all the primes up to w and multiply them together you only get up to log log n and so that's even that is negligible compared to the size of the discriminants d and then I'm going to restrict attention to only primes and this is for another technical reason primes d that are seven more eight and I'm going to want all the quadratic characters of the primes up to w to be prescribed I want them all to be plus one so this is still a large set of primes because I have I'm only imposing congruence conditions modulo the product of all the primes up to w but even the product of all the primes up to w is very small even compared to delta so if you just use the prime number theorem in arithmetic progressions this is a big set of primes of size delta over log delta the total number of primes up to this times basically a product of a probability of one half for each of the primes up to w okay so that's fixing the discriminants d I'm also going to want to account for the small prime factors of n so I'm going to break every odd number m into two parts f and h so f is the friable part of n so if all the prime factors of f are smaller than w and h has all prime factors being at least w and so now here is the modified second moment method I'm going to define f of n to be the sum over all these good discriminants so primes in a certain residue class and then to count the number of principle ideals of norm n weighted by square root of d and then divided by the number of divisors of the small prime factors of that this quantity is positive if n is represented by some binary quadratic form x squared plus d y squared with d in this set of discriminants and once again we will compute the first and second moments of this object and if we can compute these two moments then Cauchy's inequality will once again give me a lower bound for the total number of integers that are represented just the first moment squared divided by the second moment so this is now going to be the key calculation I take f m so I have to understand something about averages of r the number of principle ideals of norm n as n varies and then if I square it I'll have to understand the product of r d n and r d prime n as d and d prime period okay so here's the calculation for the first moment I can evaluate the sum over n restricting to integers that are odd with a given number of prime factors and the asymptotic takes the following shape it's a constant depending on w and this constant is just the product of one minus one over p over all primes up to w pi is just pi times the total number of integers in this set so r d of n is on average once I divide by this divisor function of f on average it's just this quantity so the first moment of f n which had a square root of d on the appearing in the numerator here would just be this constant c of w times the total number of integers times the number of discriminants that I'm summing up to compute the second moment I expand out the square in the definition of f and so what I have to understand is a similar calculation for the product of two different discriminants d and d prime so there'll be two types of terms I'm looking here at the non-diagonal terms when I expand out the square non-diagonal terms where d is not equal to d prime and then we'll also have to think of the diagonal terms where d equals d prime with sum but if I think of the non-diagonal terms because of the way I choose these local conditions on d now I can guarantee that the answer is basically the square of whatever I had before so the previous answer had a c of w over square root of d so now it has c of w squared developed by square root of d times d prime times the number of n the answer is not quite one here but the difference is just l one of the product of the two characters chi d and chi d prime times having fixed what happens at the primes of the w and this is a crucial part of the proof this is not one on the nose but it's pretty much one on average if I vary d and d prime in this progression l one chi d is a reasonably tame object I mean I don't mean things like the class number problem getting a lower bound for l one chi d for every discriminant obviously is a very hard problem but if I want to understand statistically what l one chi d does that's a very simple problem so if d and d prime vary in this set if you have a lot of discriminants to play with then typically the size of l one chi d d prime is the same as just the product of the first few primes so it only matters here that w goes to infinity as no matter how slowly it just has to go to infinity so I can approximate it typically by the product of the primes up to w of the Euler factor but the way we chose our discriminants d and d prime chi d of p and chi d of d prime of p were all going to be one so this is just one minus one over p inverse which exactly cancels with this product of one minus one over p that I already have so in other words, this extra factor that I have is most of the time going to be one and that means that if I look at the off diagonal contribution to the second moment it just basically gives me c of w squared times the number of m times the number of discriminants that I have squared we have to add the diagonal contribution where d is d prime but there are a few terms there so you can imagine that that's under control and it's not hard to get an upper bound for that and this upper bound basically all you have to observe is that once this delta is a little bit larger than two to the k, like two to the k times k to the four the diagonal contribution will be negligible in comparison to the non-diagonal contribution so that would mean that the second moment is the same constant depending on w squared times the number of integers with this given number of prime factors times the total number of discriminant squared which is very closely related to the first moment which is the same constant times the number of m times the number of discriminants so now if I use Cauchy-Schwarz the first moment squared divided by the second moment squared everything here will cancel out these will cancel out and what I get is asymptotically the number of integers up to m that are odd with a given number of prime factors which means that almost all the integers that are odd with a given number of prime factors are in fact represented by one of these binary quadratic forms of discriminant d going up to this threshold so that's a very quick sketch of the what the proof relies on but of course what I haven't told you is how one does the first and second moment calculation so I'll give a very brief indication of that so the proof to try to understand the number of ideals principle ideals of norm m in these imaginary quadratic fields we use this is a very natural idea we use the class group characters of this quadratic field use square root of d so these are just characters from the class group to the non-zero complex numbers or unimodular complex numbers and so you can think of these this of psi as a function on all ideals and it's a multiplicative function if you like on all the ideals taking values on the unit circle corresponding to each one of these so the class group this is the class group characters themselves of course form a group it's the dual group of the class group it has the same size the class number as the class group does now corresponding to each one of these characters we can form the representation number r and psi which is the number of if I sum over all the ideals of norm m and then I weight them now by the class group character psi of a we always have the principle character here which takes the value one on all the on all the ideals and then the number of representations by this principle character is nothing more than the total number of ideals of norm m the orthogonality relations for characters now tells us that the number of principle ideals of norm m is simply the sum of these representation numbers as I vary over all class group characters psi now what you would like to show is that the term here where psi is the principle character dominates and you get the principle class gets its fair share one over the class number of the total number of ideals of norm m and that all the other non-principle class group characters should contribute a negligible term so by the way this is also in my previous discussion I said that we would restrict attention to d being prime and this is kind of the reason why I'm doing it because if I restrict to d being prime I can avoid having to discuss genus characters where also something slightly different can happen for these class group characters all the class group characters that are non-principle here are non-genus characters because the discriminant is just the negative of a prime in this case now if I so for the non-principle characters we have a classical zero free region for the Hecker-L function associated to these characters and you can analyze the some corresponding sums that we need here and show that they are much smaller but if I just focus on the principle character let me just tell you how these sums are dealt with I have some kind of multiplicative function here but I just have to understand it on the integers with k prime factors and this is basically a very classical object now it can be understood by Selbert's method or the Selbert-Delange method so to understand the sum you first understand another function which is just a multiplicative function with z to the omega of n we just write down what the generating function is going to be its generating function will naturally be associated to something like zeta of s to the z times this Dirichlet L function ls chi d to the z and then you can compute what this answer is going to be so z here might be some complex number so it doesn't have a polar singularity but the answer works out essentially to be the same as if you had a pole over log n some power of log n to the z and instead of a z minus 1 factorial the only difference is that you get a gamma of z once you understand this then you can understand the sum where you restrict to integers with exactly k prime factors by using Cauchy's theorem you can take this formula and then integrate it out in z of size 1 with dz over z to the k plus 1 and that gives you the formula that I wrote down for the number of principal ideals of norm n divided by the divisor function tau of f summed over all m in this with k prime factors the second moment calculations are exactly the same of the same flavor the what we have here in that case would be two different objects r and y not the principal character for one discriminant and the principal character for another discriminant that can be understood in terms of the the data can zeta function of the bio quadratic field associated to those discriminant so it will be like zeta of s times l 1 chi d l 1 chi d prime and then l 1 chi d d prime that's where that l 1 chi d d prime term comes from and for the class group characters that are not the principal character this amounts to a rank and sell book type calculation but once again there is a zero free region for those and the rest of the proof goes through easily so that's some kind of rough indication of the proof thank you very much


I Few Perry's gone He is deceased welcome to episode number thirty eight loves him. Yeah. He's a funny guy He's we all loved him, but now he's gone a moments of silence Okay, that's enough With episode number 30 out of the fully actual podcast and second last one We got one more here next week, and then we are in the live show which is sold out Out everyone it is sold out. We'll be having merch available It's already been available. Yeah, this is this is come out the day two days after the live show before we go any further Our merch website is live. We have podcast related stuff there.  So if there's stuff there that you want to see added or you think is shit Please we can handle it.  Yes, of course. We want to hear all feedback. Well, so the live show has just been and gone now This is crazy. Wow, so we're done. Yeah. Yeah, this is like we've done filming, but it's still coming out You'll see the live show. I'm sure huge huge success. Yeah.  That's coming today and something else coming today. We got we got our wives joining us. I have a wife Michael's been away having his little mini moon. Yeah, we went to the very very very nice place and then now we have a scar, bro No, no, it was Brookfield Alice Springs spring Brooke spring Brooke spring Brooke, but We did actually managed to get on to Matt's partner.   Oh, yeah, that's a lie. Fuck.  That's a poor joke Look, she's here. She will be here. She will be here. Not yet. That's a poor joke. All right. Look We'll move on. God you guys used to be so good It's real. That's the most real thing I've ever said I wanted to be surprised when she comes in look we've been very busy We've got like well when this comes out like four weeks left But right now we have like six weeks left and we have to like do a lot of all the work that we would have to do During our break we have to do it now.  Oh Man to Australia's first ever podcast fight night Okay, we tried to get Matt involved. They couldn't do a three on three thing most podcasts are just two people I should have called out like a Producer so Michael and I still can't We'll be boxing. All right, we will be boxing two other podcast guys. I believe one of the hosts of the Proper true yarn podcasts and the other one from the dead arse podcast.  It's in April 27th next year So stay tuned for ticket information if you want to come into the Gold Coast Convention Center They're good. They're doing crazy. It's crazy.  They call it.    I'm pretty sure actually speaking of sex There's gonna be girls in bikinis fighting.  Yeah, so and it's very motivating doing this We've been I haven't missed a day of working out apart from fucking. What was it? Oh your wedding?  So I've been out of what's going on with your back It scares me.   That's completely. He's gonna fight Unsubstantiated and and so what you know where we might well There's a good chance we'll lose and get knocked out cold in front of thousands of people that'd be nice to watch But you know, it's it's for a laugh at the end of the day. I'm jealous. I wish I was fighting with you guys All right. Oh, we'll figure something out. We can get you in there Look, we'll see what we can do Matt. No, you've said it now. It's happening. It's set it on camera. Anyway, we could I'll make a call. See what see what we can do. I'll say Matt desperately wants to get involved Especially with the little people it scared me when you said that their friends with Jonathan Brown I thought Jonathan Brown would want some revenge for the brown We push because I'd be in his wake. I think he's probably more wades more than me, but That'd be terrifying to fight him But anyway, so that's what's going on.    I'm just gonna call and apologize as Margaret. Oh, that's all right It's an apology. Then it's good. Maybe have get a bit frantic at the end a bit emotional Yeah, yeah, well, that's how Margaret is so I just want to apologize for any disturbance that are Margaret may have caused Do you know what I mean?  You And yeah, that's that's it. So what so tell us about the weekend Michael.  How many first and only? But I think it was called a mini moon So we went away for a weekend and it was the most beautiful place ever somewhere in I'm gonna say Brookfield Springbrook spring brook. Did you go to pearling brook?  We cooked yourselves.  There was bees. Oh We yeah, oh, we went down. Well, they all over the ground and if Amy gets stung by a bee she dies Oh, it's her dad, but we don't know if she gets done could be so that was scary And I feel like it was like the coolest place ever to me place ever best company ever and Very good. Now you're married now. I'm gonna hang on my finger now 67% of this podcast is married and we're happy we did it we successful relationship What are you doing? What do you mean? What am I doing? What are you doing over there? Very, very happy My friends got a little girlfriend. Do you guys hold hands when you walk?  She's in there. Okay. Yeah, you love that. She loves a good hug Do you love that? You like that. Did she do you guys sleep in together? Not too much a little bit snuggle in the morning together I'm just that's getting shy You ever push your eyebrows over your eyes like do you ever push your eyebrow? Do you get nervous? Do you get nervous? Sometimes she's coming over. She's going to be cleaned. Has she ever not shaven and you've just yelled at a shave? Do you ever go like that? Have you banged your hands on the table at dinner yet? She's talking too much. No Does that happen with all of you? Oh, it happens. Have you like accidentally seen a birthmark and go oh? No, I've seen her birthmark. It's quite nice.  I didn't know she had one I'm sorry. Everyone has a birthmark. Does everyone really have a birthmark? Everyone has a birthmark. I've got one Yes, I guess it's I can't say it. I can't say it.  I think I've got one, but yeah, I think it's just mine's just here So that good good good.   Don't they I got one on the back of my leg like that Yeah, I got one there too, but see I also got that there. So they both look like Anyway, this we're talking about birthmarks. Let's move on for fuck's sake. We've progressed.  Speaking of that cracker milk thing came out. Oh, yeah, the cracker milk Halloween specials out have a bloody cheeky look Cracker milk on YouTube. We're in it. Yeah, we're all in if you look hard We're all in it. There's there's a huge announcement.   So you just have to look for yourself, all right, but On November the 7th, okay, which is now The lawnmower 5.0 Ultra Is launched So they've done one right and it was a big hit.  How you thinking or how you want it You'll never have to go to the barber again.  You can choose to wax with it. You can choose to just trim your hair You can freshen your breath with it. You can stab. You can drive in the car with it. You can drink out of it It's a flask.       How did you not know that yet? Smells nice. I don't recommend maybe doing the fire thing.     No, you get one ag1 You got your subscription. They drop at your front door.  I'm so lost.  That's straight off the scripts. Try ag1 for fuck gut Link in our description ag1.com slash fully actual and you get a free travel pack boom there you go have that That's that you could sell that travel pack for hundreds of dollars Yeah, you could easily make some money there or I just figured out a new business venture If you invoice just thousands of people for like $150 for like, I don't know electrical work or something cleaning Like a small percentage of those people will just be like, okay and and pay that invoice Then you can buy ag1 with that money that you make from these lights So now you've got a second income a third income now you could potentially build that scam up You could hire people and they could start doing it You could be invoicing millions of people a day and one percent of a million is a shitload more than what you're making And ag1 gave us those sort of ideas You could also buy get the ag1 free pack change your name get another free pack change your name get another free pack Just get heaps of free packs sell them and then get like get them right and then cancel your card Get a new card get a new card change your name Then get another free pack.  It's a jungle out there If you've experienced a lack of energy Which mat has He's always long. Oh, this is his face when he comes home. Oh hell's horse and mat Ag1 will fix that Anyway, that's enough about me. Yeah, look that was good Link in that description, man. Yeah, just drink it and you'll see. Yeah, see how good it makes you feel Don't take our word for it. Go get it done and see what you think for yourself.    Yeah, that's the end of the podcast. We'll see you guys next week And we're back matt.     Sorry guys wives. Sorry our wives. So sorry about that. Um, everyone Please Please stand and clap your hands These are our wives everybody. Welcome our wives. Have a wife We both have a wife now. Look, that's our wife now We have to be with them now for a really long time and hopefully until one of us dies a couple years at least Hate them. Yeah same. The headphones are no good. All right. So annoying Look, we're all recently It's it's night time now it's tuesday night and they're a bit tired from their big day at work. Aren't aren't you? Yeah All right. Well, look, we'll keep this we'll keep this short and sweet. All right We'll get straight into it and then we'll get yous out Why why did you guys marry us? Mon What do you mean?  Okay I married michael Um, because he makes me laugh so much. Um, what does he do that makes you laugh? Give us one example You know, honestly, it's just it's when I'm really angry. I'll be so mad Just like I don't want to be tested. I'm pms-ing.  Oh, that's a good one. Yeah. Yes. I was pms-ing hard Like I I can turn into like a like a raging bull like it's kind of scary. I think I need medication I More no and um, yeah, so we were shopping around for like that last minute stuff for um The wedding and as you can imagine michael's a big big help We're the wedding planning.   I'll be there soon. Yeah, I'm not a problem It's like pretending there's like cutting boards like this meeting that is in on the phone And these women are just walking past like slowly just looking at him really concerned And he's like, oh, yeah, I've got to go when he sees me and it just just cracked me up And then I was just out of my bad mood. Yeah, so that's the key for a while Sometimes you can go the other way and it can make you know, that's only rarely it's a risk. It's a risk Yeah, it is a bit of a risk, but no, you um always chirp me up. What what matt? What do you fuck? It's scoffing I think it's oh Yeah, I think Surely I can't I can't think of something. It's pretty much daily It's just like, you know, I think it's just things like I've just asked you the same thing like 80 Thousand times and you just still haven't done like that one thing. I was like, you know, just take the kitty litter out It's like, yeah, yeah, they just won't take litter out my surgery to take litter out like yeah Just it's just like the other day when I was at like the coffee shop She wanted me to go to a get coffee and it was like two minutes down the road But I went to one that was half an hour away. Oh my god I didn't understand why I was I thought that was the only coffee shop I said that the crepe store has the coffee beans and so he goes half an hour to new farm And I'm like, where are you?  I was like, what crepe store is in new farm? They both have the word new in it. So it confused me That is confusing. I'll give you that There was no crepe store. Yeah I thought the crepe store was the cafe, but yeah, I should have listened more Look, you guys are um, look you're with us for life now, right?  Why? I don't know She married me because she's tired You're very funny, babe You both are very tolerating Yeah, there's some good. Anyway. All right. Look, let's move on. Yes.  Yeah, I know All right Now let's get into some of these questions. All right It just be as honest as you're like Now there's some of the Now before we even get into that though, have you guys does Michael tell you what we film for the website? No, never. I never ask. I just I can't I just can't do it. What do you think? What do you think it is? Well Accidentally, um, when Michael's approving different things like last night There was just a picture of you know, both your arses like glued together with James like laughing like really happily And I don't that so it's just it's just stuff like that.    It's it's comedy It's an attempted comedy and we have a very very heavily influenced Would you ever watch them? Yes. Yeah, I I watch it for a reaction sort of But I don't know you're married. I think Amber will be very grossed out Yeah, yeah, I think we'll have to pick and choose a few especially if you think about like the the dinner date one was like Whoa, I think I love the beginning of that. That's the one I like.   Well, you don't let me Well, and well even just in general like the social media vid you're like, I'm not watching that like she hears me scream She's like, no, I can't see it. I don't want to see you on pain. Yeah, I think it's funny Yeah, mon always laughs.  I got Marty good today.  I think me. Yeah, that was what snake plant That thing but even worse today. It was like another plant What's that? What was that was that today plant on the back? Yeah, we tested which plant hurts the most I should have got your cactus There was a cactus in there. All right. It's not ccl Shout out All right guys, let's get into these questions, right? Brett Williams. Hi, Brett. How are you, Brett? Welcome to the show Oh She's taking that job question number one. What stunt slash activity has made you the most angry? Oh, no, actually, I feel like yeah, yours is easy. Yeah, no, I think it was just the um, you know I think we spoke about this um briefly last time was just yeah when Michael and I were like two months into into dating and he had the um vinegar up his arse But it was like excruciating pain for like about a week It was like bleeding from his bum like like non-stop and it was like real real writhing around and I remember marty You know looking very guilty at the hospital and I was like, you know, obviously you didn't do it on purpose But I was also like how didn't you think this was going to be going bad? Yeah, we even called james's mom and asked james sort of be fine, too We just we need to order it down and now I'm like blast oise and because we'd heard of people doing vinegar enemas before Hadn't we pretty sure Enema's a different to you know, bicarb soda or something. Yeah, I think that really reacted with you I think I was just mad about the idea of you know, you having a coloscopy coloscopy colonoscopy Dude, you know what I mean? I was stressed about it because I remember your dad was like Michael You might have a shitbag for a shot. I was like, oh my god That's like that's it. That's it Oh, and then the man deranged the eye Elevated our content as well. That was annoying Colonoscopy bag that would elevate our content. Yeah, it would be it would be good for comedy But like just life in general it would make things so much harder.   Yeah, let's do it Yeah, you know what less.  Nothing. I don't think anything's made me angry. No, I haven't been angry. I think I was just upset You know, what about his eye when he almost lost his eye when James hit me. But yeah That was bad. And when you slipped over to with your back, there was a bad one But oh that was a bad one.  All right, pete ryan How do you feel about being the queens of the 13 year olds?  Oh, that is so lame. Yeah, that's He's still have you seen him since no, but I would love to yell at him. He'd just be looking at you and go. That's the queen All right, next question. Yeah, I should Um, you didn't even ask the question. Yeah, it's just kind of Oh, well, I wanted to answer. What is it? I feel good Crowns for all of us Made by 13 year olds You know, they're not like children. Yeah, they're like they're young adults. They are they're old enough to work They are they are.  Well straight away what you don't know, doesn't it? Exactly, right? It's good for the immune system.  Man's game is not working Don't buy it No, buy it. It does work. We just didn't have it in stock that day Oh my god Yeah, so that doesn't really we use yognog from um from lush, but no michael is not a believer in in um soap So yognog, I am shampoo and conditioner. No Okay, that's gross No one washes their hair If you guys are shitting on each other you should That's what I mean. So when you guys had the barbecue Look, we're not shooting on each other's heads, babe. Yeah, there's no shitting on his head Oh, actually, yeah, there was the condom one. Oh, yeah, we are shitting on each other's heads. I forgot about that But we had a condom. It was safe and it's funny. It's it's it's anyway. Let's move on. It's fine if you wash Yeah, yeah, it's true. Just wash yourself and it will actually as well. I do wash his hair That's how he gets clean. Yeah, it is nice having I must say having a wife for the bag to wash you It's very good. It's very good. Here's a good question. Good feature about wives is they wash you. Here's here's a great question Have your friends and or family ever been concerned about the fact that you're With marty and michael because of the things they do Mine are proud for now. What do you mean for now? No Yeah, your dad's in love with mine. Yeah, if they watched the website videos mum would be very Yeah, mons family is very supportive. No. Yeah. Well, the website video is very very niche comedy. Let's not No, it's fine most I'd say 99.9% of Women over women in general would probably find that our content fucked except for there's a lot of rad chicks out there That's subscribed. So thank you. Um, but yeah, I reckon well. Ella amber say it, but oh man. I feel so supported It's very cool. The family's so very good. It's so nice because we our family wasn't even that supportive Yeah, like until like your family's better than our families Yeah, your families.  Yeah.  I know joshie loves your stuff. Yeah No, they've been very lucky because man my sister loves a podcast Simone. Oh, really? Shout out shout out shout out you get a shout out to the fam All right Um, this is a question for us. Michael. Chevy lia said are there any stunts you don't tell your partners about?  Like it's I think it's all cool to do I think I only tell mine when she asked me. She says, oh, what did you film today?  So it's like you've actually been tortured It's like, you know in a scene in a movie where the slave takes his shirt off And then the woman's like, oh no, you know, that's kind of It's like that but weekly But yeah, I can I just feel bad because I see her face.  He's coming back at it though recently We played a 5050 game today and like Like just flipping a coin and he won like 10 times in a row. It was a good job. Yeah. Yeah. Well done with the 5050 I hurt you too. Yeah, you hurt me. Yeah. Sorry, man Anyway Next question when will monon amber be in charge of inflicting pain in a video which spouse hurts more?  We swap partner. I mean, we already do that at home. Don't we Michael? Oh, no Domestic violence is not funny if you need help call blah blah blah I reckon we could do it. So Yeah, literally you do the punishment then you do the punishment and then we just assess it Three different Yeah, I think I think you both hurt us. I don't know if I'd be I'd actually hurt. Yeah, I don't think I can't hurt Marty I'd oh well then you could like obviously you'd go hard on Marty then you'd go hard on me Yeah, oh mon is more powerful. Oh am is more powerful.   You're better upper body. I'm lower body What you reckon you can kick and you can you can swing your arms. Yeah, that was violent. It was like impressive Yeah, my wedding dress is quite heavy, but man, I didn't have any trouble lifting that thing up over my head showing her underwear Yeah, I just got my period too. Literally. I do then it happened. I do blood. That's why they were red at the same time No, for real. I got it at the ceremony too. What's that? Sorry L3 The whites were were white.  Hey, I don't like blood It makes me uncomfortable. Okay All right. What about this? This is a serious question. What is your favorite color? You know mine. Yeah, surely you don't mind It's brown Yeah, but no one's got the favorite color brown. Is it really?  Pink. Yeah, what's like like pink. That's a lame question. Yeah. Yeah. So look, that's that's what I come up with That's what I come up with. How about let's talk about the wedding? So We're getting ready You can talk about that all day. I can I can I really like we're away and she's like, what do I have to look forward to now? I was like, oh look divorce We'll just do a wedding every year Renew our vows. Oh man. Yeah, because our beautiful celebrant said my vows accidentally Yeah, well, you can't have it perfect, but you can't have it perfect Yeah, yeah, well I didn't notice it.  I guess I'll make something up. Yeah, I guess I did block that. What is The most annoying thing about Michael just an annoying thing about Michael Um Yeah, I just have to repeat myself sometimes What about my what about watching movies with his listening skills?  Graham Hancock. Graham Hancock. Yeah. Yeah.  I can it's like worms, but we don't talk worms But yeah, I'm very good at worms. We all know that I could destroy worms and I don't even know what it is Oh man, imagine if we could play worms together. Oh my god, maybe you should show have you never showed her what worms think I think I showed her fortnight No, I won if you I won a match in front of her and I think it made me less sexy So I've kept gaming away But yeah, I was number nine in the world worms, babe I mentioned it in the speech is that the wedding No, I know you mentioned a lot.  That cannot be true when I don't I don't think it is Yeah, it was exaggerated a lot of it was exaggerated embellishment But yeah, there was There was a lot of worms talk wasn't there. Yeah It's so cool. I was number nine top 10. Yeah, what's annoying about me? I am just very annoying when you like hold me down and I'm trying to get away that would be It's like and I have to wait until he like stops She's literally I just have to like holding her hand gently She's I've literally conditioned her that she has to pull her hand away like as fast as she can every single time I'm touching her or you or I'll grab it. Yeah, it's just reflex. I just grab it and then I hang onto it Like right now I'm just so much stronger than she is. It's just hard not to use it You know what? I reckon we're on par.  And this is our wedding night. I told Marty I fully regret this and I'm sorry Yeah, you do it a lot.  You know, hey, babe. Like, you know really early in the morning.     Oh, I'm still thinking The one thing that I normally hate in people No about me. No, no, but this is one thing you do that I would Criticize other people so hard for I can't stand it when people eat loudly But you eat loudly and I think it's so cute I think it's like it's the cutest thing in the world And I think that's like for me to normally hate someone so much for doing that And then you do it and it's like I love you so hard.  That's wife material Because it's like normally you if it's not an annoying thing though, you love it.  What is annoying? Um, I'll go Please don't I'm scared.  It could be anywhere And she won't have any memory of where she put it.    No, he's a beautiful kisser What about me mon? I'm pretty fucking. Yeah, you were very good. The first thing that mon said about you marty was Man, is he a good kisser? Hey, well, I think matt got a photo of us the first time we where was it?  He was it wasn't even invited. Yeah, it was the first time we kissed that Yeah, no, I'm pretty sure we'd kissed before that Oh It was it was like Mon was just house sitting and I went over to the house and invited matt to come over that's when we first started talking about the podcast Yeah, the podcast and you were filming him. Yeah matt was always filming us like always trying to be real sly about it Always be kind of looking away at his phone in weird places.  Yeah the best kiss rather of a kiss That's right boys I'm actually like an insanely good kisser. I already know that I know too Mon's always mackin on me Whenever she's got you know something So you guys can kiss Ours is like Yeah, I haven't kissed marty with tongue in years. We don't kiss with tongue.   You shouldn't have done it. That's pretty silly It's your own fault. So welcome and I love you and that's that Um, yeah, thank you for marrying us and let's watch some website videos soon I want to yeah, I want to watch them and you guys should beat us as well I'd love to show them. I'm genuinely excited to show them the pistilery now. Oh, I think amber won't like that one Why because you don't really do anything gross. It's me that does the grocery Yeah, but it's like it's not that gross compared to some of the other videos. You know what I mean? Yeah, yeah, I want to see how It's like imagine like a winery, but they're all like it's different pisses Who's are they? And you drink them Just sips at them. Oh, you skull couple. When was that? That was a while ago. Were we together? Yeah, yeah No, no, I don't think we were babe. Okay film just before man. Do you drink them babe? No, I can't do the pistol. I can sip it, but I can't do the open my throat up and pour it down You drink his vomit. Yeah. Oh, yeah. That's one thing that you've done. That's worse. Yeah. Yeah Like I said, I remember I was taking a story for my business and I could just hear you guys in the background vomiting Then you said you drank it.   Have you tried your poo? Have you have you I haven't I think when I was a kid. Oh, yeah. Well, yeah, I have to really. Yeah But not interested.  No, I must be really young. I used to eat cat food too But not wet cat food dry cat food. Yeah, the biscuits. Yeah, the biscuits aren't too bad. Dry is okay. That's normal It's a bit of kangaroo Is it actual kangaroo in it? They've got different flavours. I don't know.  He got so fat. Yeah, I don't think it's good for you It's good for humans though Anyway, so if you want some cat food Ambino's um whiskers isn't too I'm joking. I don't know the brand.   I have Fuck. No, I did but I just wasn't 12. I thought we had a connection Yeah, like 4? Yeah You'd hope so. Well, I was 20 so that's a little too late. What did it taste like? It tastes like strength I am intrigued.  It takes a certain mental strength to be able to do these things though Like like there is no one else in the world that can do these things. I reckon I could do that But if you're in tears. He would never be able to do. Yeah, what he does. Maybe my own. Not one person in the world I'd rather eat my poo that I would drink my pee No way. Really? 100% My poo's so stinky wiggie. Oh, it's a stinky wiggie poo poo.  Oh, yeah It's bad Oh This is like delicious.  I'm kind of what does anyone have any piss? Oh, yeah Does anyone need to piss?  Anyway, thank you guys for coming on And um, thank you. I know you're tired and busy. Thank you guys. Thank you for having us. Thank you for inviting us here today Now there is one quick competition. We wanted you guys to do. Um, just a Fine we'll make out Matt, put it down He's holding a gun No, there's not really I just wanted to um annoy him on. Oh, thank god. Yeah, you guys are friends. I would have won anyway.  All right, there are two episodes left before the live show People who are at the live show they know They know who went who went so maybe keep it a secret or something like don't unless I win right now Which I reckon I will yeah. Yeah, but still Yeah, true. Look it could more than likely muckers. There's no way you're gonna win through to look. I might have Just for Entertainment values kind of tip the scales into matt's failure here. Why would you do that? Well because for entertainment matt Don't I'm not pitying you don't worry So this competition as you all know is for the very important Bottle of matt's a mint which is sitting in that cardboard box right there. Okay It has been it has taken it's there's generations of future human beings in there.  It's like That's never been done before if you poured that into a girl, would she get pregnant? No, she'd probably die immediately of infections infuctions So anyway, 1917 to michael and today Good movie We test Who knows more about concrete?  Yeah. Yeah matt. Look, you don't need to explain it All right.  I'm not saying that I'm not even trying to be that I'm not saying that I've put it completely in your favor I'm saying that I've leaned it slightly in your favor. Okay You were around concrete a lot No, I'm not even around it. Look you talk about it. I'm okay. Yeah, that's fair. You talk about it That's fair All right Question number one This is gonna be so remember matt or michael. I should really yell it out. Yeah, you got to yell your own name out What color is concrete michael? gray One nil Wait, that's negative What it was called gray. No because concrete comes in colors It's all come also comes in off white. All right. Look one or say concrete is gray would be a mistake a mistake All right. Look it also comes in exposed colors, which is what's just different colored rocks And what about polish? Do you like the polish? I like polish, but that's not a color. It's just a polished finish See, okay. This is fucked. I don't know. I don't want to get technical But it doesn't all come in gray.  Look question number two. It's one all. I'll give you both a point there What is concrete most widely used for michael? foundations of buildings end roads no not roads foundations of buildings and You can't say two things is a foundation of buildings or what concrete slabs to build things on top of Hey, you said like three different answers. They're the same thing just differently. They're not Concrete foundations for buildings is one thing. Concrete slabs is one thing and what's the other thing you said they're commonly most used for the Concrete slab for building something. All right concrete slab. Matt. What's your answer? What's the most concrete most commonly used for most widely almost widely used for it's got to be house slabs Copy my answer much Used building material in the entire it's most widely used building material In the entire world. That's what it is. It's a building material. So it's most widely used Building material in the entire world. Yeah, no, but that wasn't your question. What's it most commonly used for building? Yeah for building material You're both wrong. You're both wrong. You did neither of you said building material sand and senior witchcraft who made this Now reveal concrete Revellio is super popular as we know, right? So question number three concrete is super popular. Like I said Now the reason it's so popular and everyone loves it so much is is because It is resistant of two things that not many other materials are What are they? What is concrete? That's Michael. It is resistant to water And it is also resistant to air What are your answers? It's not bad. It's not a bad guess It's definitely resistant. Oh, well, it's sort of resistant to water. But yeah, it's resistant to water and God, I was gonna say like, um Yeah, there's a very good answer. I have to choose something different then Um, yeah, I don't know what the other thing would be.  What do you have a thing in the sky? Oh, so you're talking about you're both right about water Fire was the other answer I was looking for Of course I was close son on fire. Yeah, I was close.   It burned.  Yeah, that blew that blew up Maybe that's because it was hot wood. Yeah, those buildings in 9-11. Yep. Well, those are the steel beams, right? Apparently they can melt it at a very high degree. Sorry What's the score? It's uh, one and a half all one and a half What are the three things in concrete? Matt man I'm gonna get this wrong It's gonna be what the makes concrete. Yeah, it's got to be cement water sand Perfect. Oh my god. That's crazy.   What is that sand cement sand water cement? Isn't cement concrete? No, it cements the power Big misconception Michael my dear that concrete is not cement. Cement is a product in the concrete. Oh, no This is fucked. I thought you might do a fun question like how many cubic meters are in the burge califa. That'd be cool You know that no, but it would be a fun question to try and guess Maybe that's fucked man. Yeah How did all right, it's two and a half to one and a half to matt. So I'm coming to the end of this Shit, I'm so sorry everyone.  Invented cement. Oh no Michael I'm gonna say andrew johns It's pretty close. Actually pretty close. Really? Yeah It's common name. Um, I'm gonna say I can't think of one person, but I'm gonna say the The uh, the romans invented it. That is true But there's one person here. Julius Caesar. Joseph Aspiden.  That was never gonna happen close to joe to johns joe joseph Yeah, whoa, holly andrew's a bit joseph. Really a letter in there that's similar to that johns But yeah, well done matt. All right. Wow. What a riveting game that one was never ever Crazy, that's crazy. It's three and a half points to one and a half matt brown wins this week.  Now it could still be 19 all next week audience You know that that was that was fucked. That's not fair. I've really won already Well, it's kind of fair. You got to do the hair styling. See You've got hair. I've got no hair.  Yeah, but they're trained hairdressers. Okay You at least had training on your long unwashed hair unless amber washes it. Look. Yeah. Well, she does sometimes She actually said that before. Yeah, I never washed my hair. She does that even I have to wash my hair What wives should do Scalp, um Anyway, look. All right, you I'm still winning. That's fine. Well done.  What movie did you see on the weekend? I'm gonna say warlock three killers of the flower moon. Was it? Yeah, that's what it was. Is that really the name of it?  Hey, why is it called that? Do you know? I don't know I don't it's a new leo movie. It's like three and a half hours long.  Who directed the newest one martin scorsese Yeah, another all the all the big directors.  I think it's called killers of the flower moon Say the name of the director martin scorsese.  What marcus cork martin scorsese Pretty sure that it's probably not his real name, but I'm pretty sure he's italian of some kind.  How do you not know then? How do you not know his name? I know that one that did the pulp fiction steven billburn. That was actually quentin tarantino Yeah, I know that one steven billburgo one two And I know james cameron because he did titanic and leonard recovery is in titanic Titanic's probably one of the best films ever. They should make a titanic too.  They should make titanic too. Sorry about that segment and it's 18 to michael Let's Say one thing Titanic is actually the second movie about the titanic I'll leave you with that. I'll leave you with that Don't don't matt's tinder adventures. Jesus. It's been done is what i'm trying to say. Hit it matt T-i-n-d-o we have matt's tinder Matthew brown is lost control now these women will lose their souls Oh This is a segment where michael and I have taken over matt brown's tinder Even though he's technically in a committed happy healthy relationship michael and I still want to manage to get some plant bees plant seeds because let's be honest Even just some side bitches. No. Yeah, baby. No, I I think I love my girlfriend Did you say I love you he did He did don't yeah, don't put that bad that bad vibe out there. I think this could be this could be the one man How did you say it?  You won't tell us no way it's personal remember your little thing you cut before yeah, but that's saying I love you I'll say how I told I told amber after she told me And I think it was like a couple days later.  No, she she did she walked up. I was like, oh my god. I think I love you and she's like Are you matt?  I did. I did.  I was doing it in a joking way I'm gonna ask her now because you're not being you're not being forthcoming. What are you gonna do in tinder ends? What do you mean going? Well, they were at the end of this season. We're gonna get you security guys from grinder Anyway, let's move on. All right.  He was the one who was depressed and always put heaps of salt on his meals Oh, what an opening line Yeah, I'm just really proud of him He worked so hard to make it in the acting world and when he landed that job our whole lives changed He even started getting recognized in the street sometimes. I love my dad so much. Are you close with your dad? I am really close with my dad with my whole family really. Oh, that's great My dad is my best friend. We're learning how to dance together at the moment We have we have to go to lessons. Huh mom not so much.  She always tries to join in with me and dad But I don't know.  You can't leave me hanging like this. I'm so invested in the whole mom heading storyline Oh, it's nothing really. I just have never gotten along with mom.   She's got arthritis in her spine She can't bend over.  That's a lot of info.  I'm sorry that happened Lol literally everyone I tell these stories tells the same reaction My brother's wife didn't believe them until she met her But yeah, everyone has family stories. I guess might have just a little more colorful Once she gave me an uncooked eggs for lunch at school just a 12 pack in my bag I got bullied pretty bad that day.  Oh really? I can't tell if you're joking or not. Usually people get pretty shocked at these stories Oh wait, is it because my dad was on blue healers? Yeah, you had me at that Can't wait to get married and solve all your mommy issues Again, I can't tell if you're being serious. Can we just talk about something other than my greasy mother?  Big swollen flaps and she can't speak any English hard gash and it's splintered She spins her head around and doesn't go to church now.     Are you Muslim? You didn't say that did you? Yeah, what's wrong with that? Just relax. All right, listen to the conversation What if I was oh, that's cool I've got like five muslim mates and they're so cool. They rip bongs and start fights sometimes But they're usually really friendly. Do you want to meet them? They're great. My grandparents are muslim. They're converted. My dad's side still practice.   Yeah, I didn't think that was gonna.  Ha ha my legs are I'm nearly at a right angle.   I wasn't expecting that. They're just kids. They don't know any better Did you ever make any mistakes as a child?  She'd sing it even in public It's stuck with me forever.  I was just a child Oh, she unmatched. Yeah, she unmatched Oh This chick starts his conversation. Hey, hey, what's happening? I just saw short circuit at the house.  What's your favorite room in your house? Oh, that's deaf tomorrow problem. I love my bed. It's comfy and I miss it while I'm at work Yeah, I love my bedroom too. Favorite room is probably my collection room though I collect a lot of stuff. Least favorite is the laundry.   I never go in there unless I totally have to I'm Anyway, that is Matt's Tinder adventures guys. There's only one It's in only two more weeks. I'm really gonna just I'm putting some effort. We have one more episode and then it's live Look, there's definitely some potential there. So you've got some girls there There are you if you want I think so. I think there was some some good steps forward then There was yeah, so, you know, just don't have to act on it, but just keeping the back in mind Yeah, I think I'm gonna be good progression was made though I don't think we really need any dating things at all. I can't but do you reckon you'll get married when I don't know like two years I don't know time to tick him up around do you reckon you'll have a family? I don't know Like come on. You never open up. I'm not revealing anything yet. It's early days Yeah, but like just in general not not with your girlfriend. You said would you want can you see yourself? I've had a little brown kids Yeah, I definitely want kids. Do you ever brush your hair behind it is that's how they know you like them cry All right, guys now we move on to the questions. See here mad brown push the button don't spill the mother everywhere sleep You have all the questions and we have all the answers and we've got lots of dances for you So This is a segment where we answer the questions you guys have commented on the muddy muggle fully actual youtube channel What's the answer the most liked questions first? So once you comment your question have a scroll through and like the other questions She wants to answer. All right, buddy. Let's pump out a few little questions. Just try to put my whole mouth over the mother can And it lock jaw lock jaw. You had lock jaw didn't you? Do you have the Top question went to peter hunt Have you ever I like this Have you ever Have you ever considered calling the butcher or the random number from the billboard again? That was a highest like question Yeah, the butchers long story short. Look it got weird and then the the uh the billboard man Changed his number. Um, yeah, look the butcher. I call him and tell him it's a you know It was all a prank and stuff like that and um He just wanted to be mates. Yeah. Yeah, he just wanted to be mates. Um, and uh, yeah That's what happened now.  All right. Uh question for mighty michael matt and james. So mighty you can answer for james Um, if you'll pick an apple if you can all pick an animal to represent you in a fight to the death What animal do you pick? Like like do we get to choose or animal that's most like us? No, no, you get to pick an animal to represent you in a fight And so we're just trying to come up with the strongest animal that we can So you go lion One lion. I reckon one elephant would kill one lion. I'm going with a bear like a grizzly bear James would probably say jet James would just go as himself. Yeah, james would fight him Crocodile maybe Stomp stomp on his head bro I'm gonna be out of the grizzly in the shark and the fight is in water He's just throwing a curveball. I didn't see it come on bro. What animal are we?   No, they're like so big. You seem in the zoo No, matt would be a wombat a wombat Oh matt's a wombat Yeah, I love wombat. Yeah, they are cute. That does actually I can see you've got the wombat face All right, next question is from tablecloth 84 um I've been rewatching the chaos of the first two seasons of the podcast and was wondering would you ever do a retro episode We had a few drinks and you did all the early like a early episode stuff like um a lot of the early segments Yeah, the first season we just get fucking drunk every time We weren't used to like talking to camera like this, but we do a science time A domino's prank because a lot of the stuff we did funny segment names We can do that for an episode. That's a great one. So we can do a retro one cute little idea We get throw back to first hammer drunk.  That was fun. Yeah, so maybe next season We will definitely do a retro episode We don't we don't we don't drink too much especially because like what if it's a great episode We're super engine you guys love it and then every week And then before you know, we're alcoholics But we can do a retro throw back to old Will you get drunk setups?  Yeah wine white wine Reasling that loves a reasling from the Yarra Valley. Really? Yeah. Those those cool words That's cool. Next question is from mark howard in a seven one six one Um, he said a bunch of things, but he said what would you hope for in 2024 with this podcast on the channel? Well more growth More this year has been quite a roller coaster more than any other season.  If you have any suggestions, please do comment them down below All right, and we'll take them in to continue very very open to segments We already had a couple of good ones Which will because like obviously we can't do matt's tender segment. So that'll be dearly missed and um black book Look, I wouldn't maybe I feel like that would just get maybe I can try and and then they'll just like we'll just have to remove The real bad bits anything on Spotify the fucked one or I wonder if we should do like a matt vs. Michael number two or like somehow Maybe somebody threw one out there that didn't that actually tickled my fancy a bit because james is always a good fun to have on And uh, but then he's not always here is he? Yeah, okay on monday. So he could be If if we plan to write someone throughout they're going james vs. marty That kind of got me going a bit but I know you'd have to be here every episode. You'd have to be here every episode But yeah guys look the next season where it's gonna.  Yeah, this season.    Yeah, we have to we literally have to change. Otherwise it stops It's either change or stop But we will don't worry.  I reckon. Yeah, someone will have a heart attack.   Why are you better than doctors? Even like like anyway, Brad Pitt. I reckon I'm probably better than I'm better than I'm better than Leonardo DiCattano.  It's hard to be better than him I'm better than most things ever in the world. I think yeah. Yep I agree. That's good. Well said Um, next question is from Dean Moore zero eight. Um He did ask two things asked for a german or gibberish as of matt vs michael, but if not, can we get one at the live show?  I just want to buy it knock Um, have you guys considered going to public toilets and calling the random numbers written on the walls? Yeah, yeah, that's happening. I'm definitely I think the problem is Most people write those numbers on there because they're stitching. They're made up and most people don't answer If I call another mobile on a private number It's like a 10 chance. I'll answer.  Uh, next one is from ad victory three two nine one michael, um on the latest website video Well, it wasn't the latest, but it was the last one he saw Um, you got hit, uh, the pain scale when you got hit by an orange to your face. What was it? Oh The mandarin It's it rocks you, but it's not like painful.  Oh man.  You cop took I think it was oranges to the head You cop two to the head from luke and james and you had to walk around the corner. Just see have a break Yeah, yeah, I remember I got hit rocked by an orange to the head first shot Didn't get caught on camera. So I'm just like I can't stick around anymore.    Sorry from speaking till I finish Movies are cooler than golf. Sorry now.  I get it. All right Sorry, but if you do play golf you realize what I'm saying and like I'm right If you play golf golf is better than movies.  Maybe you should try it. Maybe you should try maybe there's something rewarding about dropping that can There were more comments saying movies are better than golf I get movies like I saw a movie last night the leo one.    Well done. Racker. That was a good finally an original horror every horror Maybe I know what's gonna happen every action. Maybe I know what's gonna happen every movie I know it's just a movie because it is it's a movie You just got a dd. You can't you can't settle down and watch something. Well, I don't I just pop my own vids on Also, I will agree with you. I'm the best golf is fun for the first nine holes Golf is fun if you can hit a ball if you can't hit a ball even if you can't hit a ball You're just going to warm your arms up. You're just swinging at the air That's not fun. I don't like swinging like this I like killing something and seeing a reward when it lands on the green and by the I don't know if you guys know this I've gotten three hole-in-ones. I pitch and putt I've seen it go in the hole from being Tens of meters away And it just goes and I don't see the ball anymore. I have to walk up and pick it out Most people have to putt. I didn't even take my putter up. I just picked it out of the hole I am really good at golf No, you're not okay. I'm pretty good at golf. I'm getting better, but you anyone can go to this Anyone can do that. Anyone can just watch a movie.  I I celebrate I do not I've seen you more angered at your game than you have been happy with I keep my head very well.   This is getting out of control. Look boys. They're both Grand hobbies. All right golf is better if you play golf. I'm sorry.   Anyway, let's let's let's move on Only people that hate movies Are people who aren't good at it are people who are blind sound like a very frustrated mind anyway I think I won that Look, I get I get where you're coming from But it's still going on I'm better, I'm better I hope he's better if you are good at it and this is sponsored by It's actually brought to you by mother Your time is there for us to waste picking up your phone was your first mistake. Ha ha ha ha It's prank call time I'm Speaking with All right, I've just come through um your survey Did you know you's got the songs around the wrong way?   I didn't understand a word you said man.  I'm speaking english, isn't it? What I'm speaking english. I don't know. What do you mean? You can't understand me, mate I what do you mean? I just told you I can't understand what you're saying Yeah, look, I'll explain it again, mate. Okay.  Is it just before you just told me it was just before mate It was late this it was late this morning. All right, and I'm telling you now I didn't drive have to drive far and this afternoon me cars conked out. All right So listen up for a second rot. I'm meant to fill it with diesel rot You's got the signs around the wrong way. I don't know. I don't I didn't I didn't I don't do this sign Mate, I don't do that. I don't do my shift and then I go home. Do you understand me now? You understand what I'm saying right now? Look and what do you mean you don't do the signs?  That's done me in mate. Your shop's done me in Huh? What do you mean? Your shop right? My shop my shop mate. I think you need to You know, I think you need to come in and speak to the manager or something. What are you talking about? You need to speak to the manager mate. Like it's your shop.  You just got to compensate me Sorry mate, that's your problem not mine. I don't do the signs. I didn't switch nothing around Mate, it's yours. It's yours. It's your shop mate. You need to speak to the manager. That's not my job, right? I'm coming in. I'll come in. Are you letting the manager know? He's got to swap the signs around mate. I can't what do you mean?  Look, I'm your boss. I'll come in. I'll come in. Oh Wow I'm sorry we should have calmed it. It's too too aggressive I apologize And but mate that's I see where you've come from All right guys. Look it's a setup.  Next week It'll be on a little bit earlier It'll be on a little bit earlier. So we'll be able to call them. They'll be open So look we got two um great options there and I just want you guys to know Uh to give us a five star review right now And and like and comment and subscribe if you if you want a lot of you watch but don't subscribe Let's see if we can get to 3k Five star reviews of spotify. That would be so cool. And remember guys the uncensored version is on spotify.