Hello, 
Is it possible to reconstruct the Riemann zeta function given the precise location of its infinitely many zeroes?
Thanks



Is it possible to reconstruct $\zeta$-function knowing its zeroes?
This is well known (Riemann could have writen it)


$$\zeta(s)=\frac{1}{2}\frac{\pi^{s/2}}{(s-1)\Gamma(1+s/2)}\prod\_{\Im\rho > 0}\Bigl\{
\Bigl(1-\frac{s}{\rho}\Bigr)\Bigl(1-\frac{s}{\overline{\rho}}\Bigr)\Bigr\}$$


Here $\rho$ runs through the non trivial zeros with positive imaginary part.


It is this what you call reconstruct?


