Effective Estimates for the Distribution of Values of Euler Products

Abstract.

We prove effective upper bounds for the almost periodicity of polynomial Euler products ${\cal L}(s)$ in the half-plane of absolute convergence. From this we deduce estimates for the roots of the equation ${\cal L}(s) = c$, where c is any non-zero complex number which is attained by ${\cal L}(s)$. The method relies mainly on effective diophantine approximation.