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Math Help - Riemman Zeta Funcion Identity

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    Re: Riemman Zeta Funcion Identity

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