Denseness results of Hurwitz Zeta-Functions with Algebraic Parameter

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.

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