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

We study the value-distribution of the Hurwitz zeta-function with algebraic irrational parameter ζ(s;α)=∑n≥0(n+α)−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+iR. This may be considered as a first “weak” manifestation of universality for those zeta-functions.