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

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