Lithuanian Mathematical Journal

, Volume 54, Issue 1, pp 74–81 | Cite as

Self-approximation of Hurwitz zeta-functions with rational parameter

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Abstract

In this paper, we show the self-approximation property for Hurwitz zeta-functions with rational parameters. Namely, we prove that ζ(s + iατ, a/b) approximates uniformly ζ(s + iβτ, a/b) for infinitely many real τ , where α, β are arbitrary real numbers linearly independent over \( \mathbb{Q} \), and s is in a compact set lying in the open right half of the critical strip.

Keywords

Hurwitz zeta-function self-approximation 

MSC

11M35 11M36 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznánPoland

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