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 Chebyshevskii Sb., 2018, Volume 19, Issue 2, Pages 368–376 (Mi cheb660)

Almost periodic functions and property of universality of Dirichlet L-functions

V. N. Kuznetsova, O. A. Matveevab

a Saratov State Technical University
b Saratov State University

Abstract: The term "universality" for functions was introduced in the early 1970s by E.M. Voronin and the meaning that is embedded in this concept is that a very general class of analytic functions admits approximation by vertical shifts of a given function. In 1975, S.M. Voronin proved the universality property for Riemann zeta-functions, and in 1977 for the Dirichlet L-function.
In this paper we propose a proof of the universality property for Dirichlet L-functions that is different from SM's proof. Voronin, based on a rapid approximation in the critical band of Dirichlet L-functions by Dirichlet polynomials.

Keywords: universality property, approximate Dirichlet polynomials, almost periodic functions.

DOI: https://doi.org/10.22405/2226-8383-2018-19-2-368-377

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UDC: 511.3
Accepted:17.08.2018

Citation: V. N. Kuznetsov, O. A. Matveeva, “Almost periodic functions and property of universality of Dirichlet L-functions”, Chebyshevskii Sb., 19:2 (2018), 368–376

Citation in format AMSBIB
\Bibitem{KuzMat18} \by V.~N.~Kuznetsov, O.~A.~Matveeva \paper Almost periodic functions and property of universality of Dirichlet L-functions \jour Chebyshevskii Sb. \yr 2018 \vol 19 \issue 2 \pages 368--376 \mathnet{http://mi.mathnet.ru/cheb660} \crossref{https://doi.org/10.22405/2226-8383-2018-19-2-368-377}