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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 25–37 | Cite as

The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2

  • Ramūnas GarunkštisEmail author
  • Andrius Grigutis
Article
  • 12 Downloads

Abstract

Let ζ(s) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality |ζ(1 − s)| > |ζ(s)| is valid except at the zeros of ζ(s). Here we investigate the Lerch zeta-function L(λ, α, s) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality |L(λ, λ, \(1 - \bar s\))| > |L(λ, λ, s)|.

Keywords

Lerch zeta-function functional equation zero distribution 

MSC 2010

11M35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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