Question 560454
Here's one:


Given the Riemann zeta function


*[tex \LARGE \zeta(s) = \frac{1}{1^s} + \frac{1}{2^s} + \frac{1}{3^s} + ...]


and its analytic continuation


*[tex \LARGE \zeta(s) = \prod_{p} \frac{1}{1 - \frac{1}{p^s}}],


Prove that all the non-trivial zeros of the zeta function have a real part of 1/2 (e.g. prove that they lie on a line in the complex plane defined by Re(s) = 1/2).