let be a function $ f(s)$ which satisfy the Riemann functional equation
$ f(1-s)=R(s)f(s) $
however there are cases that $ f(s)$ satisfy Riemann Hypothesis for its Nontrivial zeros (assumed) but has an Euler product $ f(s)= \prod _{p} \frac{1}{1-p^{-s}} $
in other cases $ f(s) $ has zeros OUTSIDE the critical line but has no Euler product
if there a geometric or Number theoretic explanation or similar for an Euler product ?? apart from the fact that taking the logarithmic derivative inside a product can be interpreted in terms of closed orbits.
