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.

We found a gap in our reasoning of the previous versions and we had to withdraw the manuscript. After major revisions, this the newest version of it