When the parameter is set to one, it can be expanded as a series whose coefficients are Stieltjes constants, and it can be evaluated using Parseval's theorem. A generalization of it is called the Hurwitz function, and it resembles a p-series. When evaluated at 2, it gives the solution to the Basel problem, and Ramanujan showed that it is equal to minus one twelfths when evaluated at negative one. 1.5 million roots have been shown to lie on the critical strip, but it is not known whether all roots have a real part 1/2, and this function is closely associated with the pr
When the parameter is set to one, it can be expanded as a series whose coefficients are Stieltjes constants, and it can be evaluated using Parseval's theorem. A generalization of it is called the Hurwitz function, and it resembles a p-series. When evaluated at 2, it gives the solution to the Basel problem, and Ramanujan showed that it is equal to minus one twelfths when evaluated at negative one. 1.5 million roots have been shown to lie on the critical strip, but it is not known whether all roots have a real part 1/2, and this function is closely associated with the prime number theorem. For 10 points, identify this function named for a German mathematician who has a namesake hypothesis
When the parameter is set to one, it can be expanded as a series whose coefficients are Stieltjes constants, and it can be evaluated using Parseval's theorem.
Riemann zeta function [prompt on partial]