## Abstract

We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts *ζ*(*s* + i*γ _{k}*),

*k*∈ ℕ, of the Riemann zeta-function, where

*γ*are imaginary parts of nontrivial zeros of

_{k}*ζ*(

*s*).

Show Summary Details# The Riemann hypothesis and universality of the Riemann zeta-function

## Abstract

## References

## About the article

More options …# Mathematica Slovaca

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Editor-in-Chief: Pulmannová, Sylvia

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Ramūnas Garunkštis / Antanas Laurinčikas

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Get Access to Full TextWe prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts *ζ*(*s* + i*γ _{k}*),

MSC 2010: Primary 11M06

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

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**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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