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arXiv · 1807.04124

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

Athanasios Sourmelidis·Jörn Steuding
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Abstract

We study the value-distribution of the Hurwitz zeta-function with algebraic irrational parameter $\zeta(s;\alpha)=\sum_{n\geq_0}(n+\alpha)^{-s}$. 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 $1+i\mathbb{R}$. This may be considered as a first "weak" manifestation of universality for those zeta-functions.

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Athanasios Sourmelidis, Jörn Steuding. 2018-07-11. On the Value-Distribution of Hurwitz Zeta-Functions with Algebraic Parameter. https://doi.org/10.1007/s00365-021-09561-2

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