Abstract:
In this talk we will discuss about the value-distribution of the
Hurwitz zeta-function
$$
\zeta(s;\alpha) = \sum\limits_{n=0}^{+\infty}(n + \alpha)^{-s}, \;\;\;\Re(s) = \sigma > 1,
$$
with algebraic irrational parameter $\alpha$. In particular, we prove effective denseness
results of the Hurwitz zeta-function and its derivatives in suitable
open strips containing the vertical line $1 + i\,\mathbb{R}$. We build on ideas
of S.M. Voronin and A. Good and this may be considered as a first
"weak" manifestation of universality for those zeta-functions inside
the critical strip. This is joint work with Jörn Steuding.