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

Athanasios Sourmelidis; Jörn Steuding

doi:10.1007/s00365-021-09561-2

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

Athanasios Sourmelidis^*, Jörn Steuding

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	829-860
Number of pages	32
Journal	Constructive Approximation
Volume	55
Issue number	3
DOIs	https://doi.org/10.1007/s00365-021-09561-2
Publication status	Published - Jun 2022

Keywords

Approximation by algebraic numbers
Universality
Zeta-functions

ASJC Scopus subject areas

Computational Mathematics
Analysis
Mathematics(all)

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10.1007/s00365-021-09561-2

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abstract = "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.",

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AB - 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.

KW - Approximation by algebraic numbers

KW - Universality

KW - Zeta-functions

UR - http://dx.doi.org/10.1007/s00365-021-09561-2

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JO - Constructive Approximation

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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