Riemman Zeta Funcion Identity

**everk** · September 14th 2011, 07:09 PM

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

**gosuman** · September 14th 2011, 09:24 PM

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.

**Petek** · September 17th 2011, 04:53 PM

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

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