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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

Full text: PDF file (526 kB)
References: PDF file   HTML file

UDC: 511.3
Received: 24.04.2018
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}


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