On the Value-Distribution of Hurwitz Zeta-Functions with Algebraic Parameter

Abstract

We study the value-distribution of the Hurwitz zeta-function with algebraic irrational parameter \(\zeta (s;\alpha )=\sum _{n\ge _0}(n+\alpha )^{-s}\). In particular, we prove effective denseness results of the Hurwitz zeta-function and its derivatives in suitable strips containing the right boundary of the critical strip \(1+i{\mathbb {R}}\). This may be considered as a first “weak” manifestation of universality for those zeta-functions.