Riemman Zeta Funcion Identity

Hi everyone,

I need to compute this product in terms of $\displaystyle \zeta(s), \zeta(s+1)$ where $\displaystyle \zeta $is the riemman zeta function

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

I apreciate any help!!!.

Everk

Re: Riemman Zeta Funcion Identity

You might play with the Weierstrass factorization for sin:

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

and the functional equation:

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

Sounds like a fun problem actually.

Re: Riemman Zeta Funcion Identity

For the sake of avoiding duplication, I replied to this question here.