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Mathematica Slovaca

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Volume 68, Issue 4

Issues

The Riemann hypothesis and universality of the Riemann zeta-function

Ramūnas Garunkštis
  • Institute of Mathematics Faculty of Mathematics and Informatics Vilnius University, Naugarduko 24 LT-03225, Vilnius, Lithuania
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/ Antanas Laurinčikas
  • Institute of Mathematics Faculty of Mathematics and Informatics Vilnius University, Naugarduko 24 LT-03225, Vilnius, Lithuania
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Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0141

Abstract

We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s).

MSC 2010: Primary 11M06

Keywords: Riemann hypothesis; Riemann zeta-function; universality; weak convergence

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About the article

Received: 2016-09-08

Accepted: 2017-07-30

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Federico Pellarin


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 741–748, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0141.

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