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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.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Erikas Karikovas

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614, Poznán, Poland

    Łukasz Pánkowski

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  1. Erikas Karikovas
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  2. Łukasz Pánkowski
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Correspondence to Erikas Karikovas.

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Karikovas, E., Pánkowski, Ł. Self-approximation of Hurwitz zeta-functions with rational parameter. Lith Math J 54, 74–81 (2014). https://doi.org/10.1007/s10986-014-9228-x

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  • DOI: https://doi.org/10.1007/s10986-014-9228-x

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