The most useful algorithm for computing it is named after Odlyzko and Schonhage, and is far more computationally efficient than the algorithm named partly after Siegel.  
The most useful algorithm for computing it is named after Odlyzko and Schonhage, and is far more computationally efficient than the algorithm named partly after Siegel.  Beukers' integral is used to approximate one value of it; that value was proven to be irrational and is known as Apery's constant.  Trivial zeroes exist at every even negative integer, while if its nontrivial zeroes have real part equal to one half, and thus lie on the critical line, its namesake hypothesis is satisfied.  FTP, name this function from number theory, linked to the prime number theorem, named after a German mathematician who was also the namesake of a method of summation in calculus.
The most useful algorithm for computing it is named after Odlyzko and Schonhage, and is far more computationally efficient than the algorithm named partly after Siegel.  
{Riemann} Zeta Function