# Riemman Zeta Funcion Identity

• September 14th 2011, 08:09 PM
everk
Riemman Zeta Funcion Identity
Hi everyone,
I need to compute this product in terms of $\zeta(s), \zeta(s+1)$ where $\zeta$is the riemman zeta function

$\prod_\rho 1- \frac{s^2}{\rho^2}$ and $\rho$ goes over all non trivial zeros of $\zeta$.

I apreciate any help!!!.
Everk
• September 14th 2011, 10:24 PM
gosuman
Re: Riemman Zeta Funcion Identity
You might play with the Weierstrass factorization for sin:

$\sin(\pi s) = \pi s \prod_{n=1}^\infty \left(1-\frac{s^2}{n^2}\right)$,

and the functional equation:

$\zeta(s) = 2^s\pi^{s-1}\Gamma(1-s)\zeta(1-s)\sin(\pi s/2)$.

Sounds like a fun problem actually.
• September 17th 2011, 05:53 PM
Petek
Re: Riemman Zeta Funcion Identity
For the sake of avoiding duplication, I replied to this question here.