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 + i R . This may be considered as a first “weak” manifestation of universality for those zeta-functions.