Dyson's transform is a fundamental technique in additive number theory, it was developed by Freeman Dyson as part of his proof of which theorem?
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Dyson's transform Dyson's transform is a fundamental technique in additive number theory. It was developed by Freeman Dyson as part of his proof of Mann's theorem, is used to prove such fundamental results of Additive Number Theory as the Cauchy-Davenport theorem, and was used by Olivier Ramaré in his work on the Goldbach conjecture that proved that every even integer is the sum of at most 6 primes. The term "Dyson's transform" for this technique is used by Ramaré. Halberstam and Roth call it the τ-transformation.
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Freeman Dyson Freeman John Dyson {'1': ", '2': ", '3': ", '4': "} (born 15 December 1923) is an English-born American theoretical physicist and mathematician. He is known for his work in quantum electrodynamics, solid-state physics, astronomy and nuclear engineering. He theorized several concepts that bear his name, such as Dyson's transform, Dyson tree, Dyson series, and Dyson sphere.
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Fundamental theorem The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming of such a theorem is not necessarily based on how often it is used or the difficulty of its proofs.
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Kinoshita-Lee-Nauenberg theorem The Kinoshita–Lee–Nauenberg theorem or KLN theorem states that perturbatively the standard model as a whole is infrared (IR) finite. That is, the infrared divergences coming from loop integrals are canceled by IR divergences coming from phase space integrals. It was introduced independently by and .
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Minkowski's second theorem In mathematics, Minkowski's second theorem is a result in the Geometry of numbers about the values taken by a norm on a lattice and the volume of its fundamental cell.
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Analytic subgroup theorem In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s.
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Transcendental number theory Transcendental number theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.
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Carmichael's theorem In number theory, Carmichael's theorem, named after the American mathematician R.D. Carmichael,
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Euler's theorem In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if "n" and "a" are coprime positive integers, then
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Roth's theorem In mathematics, Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that a given algebraic number formula_1 may not have too many rational number approximations, that are 'very good'. Over half a century, the meaning of "very good" here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of , , , and .
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Bohr–Mollerup theorem In mathematical analysis, the Bohr–Mollerup theorem is a theorem named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it. The theorem characterizes the gamma function, defined for "x" > 0 by
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Discrete logarithm In mathematics, a discrete logarithm is an integer "k", solving the equation "b" = "g" , where "b", not being the identity, and "g" are elements of an arbitrary group (not necessarily connected with integers at all), where the group operation is denoted as multiplication, and thus an integer "exponent" "k" induces the usual meaning of "k"-fold multiplication of a group element with itself. In case such a "k" exists, it is denoted as "k" = log "g" . Discrete logarithms are thus the group-theoretic analogue of ordinary logarithms, which solve the analogue equation for real numbers "b" and "g", where "b" ≠ "1" is the base of the logarithm, and "g" > "0" is the value whose logarithm is being taken.
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Hermite–Minkowski theorem In mathematics, especially in algebraic number theory, the Hermite–Minkowski theorem states that for any integer "N" there are only finitely many number fields, i.e., finite field extensions "K" of the rational numbers Q, such that the discriminant of "K"/Q is at most "N". The theorem is named after Charles Hermite and Hermann Minkowski.
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Kummer theory In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of "n"th roots of elements of the base field. The theory was originally developed by Ernst Eduard Kummer around the 1840s in his pioneering work on Fermat's last theorem. The main statements do not depend on the nature of the field - apart from its characteristic, which should not divide the integer "n" – and therefore belong to abstract algebra. The theory of cyclic extensions of the field "K" when the characteristic of "K" does divide "n" is called Artin–Schreier theory.
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Rankin–Selberg method In mathematics, the Rankin–Selberg method, introduced by and , also known as the theory of integral representations of "L"-functions, is a technique for directly constructing and analytically continuing several important examples of automorphic "L"-functions. Some authors reserve the term for a special type of integral representation, namely those that involve an Eisenstein series. It has been one of the most powerful techniques for studying the Langlands program.
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Grunwald–Wang theorem In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element "x" in a number field "K" is an "n"th power in "K" if it is an "n"th power in the completion formula_1 for all but finitely many primes formula_2 of "K". For example, a rational number is a square of a rational number if it is a square of a "p"-adic number for almost all primes "p". The Grunwald–Wang theorem is an example of a local-global principle.
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Lindelöf's theorem In mathematics, Lindelöf's theorem is a result in complex analysis named after the Finnish mathematician Ernst Leonard Lindelöf. It states that a holomorphic function on a half-strip in the complex plane that is bounded on the boundary of the strip and does not grow "too fast" in the unbounded direction of the strip must remain bounded on the whole strip. The result is useful in the study of the Riemann zeta function, and is a special case of the Phragmén–Lindelöf principle. Also, see Hadamard three-lines theorem.
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Odd number theorem The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology.
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Fundamental theorem on homomorphisms In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism.
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Schur's theorem In discrete mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of . In functional analysis, Schur's theorem is often called Schur's property, also due to Issai Schur.
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Additive identity In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element "x" in the set, yields "x". One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.
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Automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group "G" to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup formula_1 of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.