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Mat. Sb., 2019, Volume 210, Number 12, Pages 98–119 (Mi msb9194)  

This article is cited in 2 scientific papers (total in 2 papers)

Universality of $L$-Dirichlet functions and nontrivial zeros of the Riemann zeta-function

A. Laurinčikas, J. Petuškinaitė

Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

Abstract: We prove a joint discrete universality theorem for Dirichlet $L$-functions concerning joint approximation of a tuple of analytic functions by shifts $L(s+ih\gamma_k, \chi_1),…,L(s+ih\gamma_k,\chi_r)$, where $0<\gamma_1<\gamma_2<\dotsb$ is the sequence of imaginary parts of the nontrivial zeros of the Riemann zeta-function, $h$ is a fixed positive number, and $\chi_1,…,\chi_r$ are pairwise nonequivalent Dirichlet characters. We use a weak form of Montgomery's conjecture on the correlation of pairs of zeros of the Riemann zeta-function in the analysis. Moreover, we show the universality of certain compositions of Dirichlet $L$-functions with operators in the space of analytic functions.
Bibliography: 31 titles.

Keywords: Montgomery's conjecture on correlation of pairs, Riemann zeta-function, Dirichlet $L$-function, nontrivial zeros, Voronin's theorem, universality.

Funding Agency Grant Number
ESF - European Social Fund 09.3.3-LMT-K-712-01-0037
The research of the first author was funded by the European Social Fund according to the activity “Improvement of researchers' qualification by implementing world-class R&D projects” of Measure no. 09.3.3-LMT-K-712-01-0037.

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DOI: https://doi.org/10.4213/sm9194

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English version:
Sbornik: Mathematics, 2019, 210:12, 1753–1773

Bibliographic databases:

UDC: 511.331
MSC: 11M06, 11M26
Received: 13.11.2018 and 25.04.2019

Citation: A. Laurinčikas, J. Petuškinaitė, “Universality of $L$-Dirichlet functions and nontrivial zeros of the Riemann zeta-function”, Mat. Sb., 210:12 (2019), 98–119; Sb. Math., 210:12 (2019), 1753–1773

Citation in format AMSBIB
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\by A.~Laurin{\v{c}}ikas, J.~Petu{\v s}kinait{\.e}
\paper Universality of $L$-Dirichlet functions and~nontrivial zeros of the Riemann zeta-function
\jour Mat. Sb.
\yr 2019
\vol 210
\issue 12
\pages 98--119
\mathnet{http://mi.mathnet.ru/msb9194}
\crossref{https://doi.org/10.4213/sm9194}
\transl
\jour Sb. Math.
\yr 2019
\vol 210
\issue 12
\pages 1753--1773
\crossref{https://doi.org/10.1070/SM9194}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078461200}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Laurincikas A., Siauciunas D., Vadeikis G., “Weighted Discrete Universality of the Riemann Zeta-Function”, Math. Model. Anal., 25:1 (2020), 21–36  crossref  mathscinet  isi
    2. Balciunas A. Garbaliauskiene V. Karaliunaite J. Macaitiene R. Petuskinaite J. Rimkeviciene A., “Joint Discrete Approximation of a Pair of Analytic Functions By Periodic Zeta-Functions”, Math. Model. Anal., 25:1 (2020), 71–87  crossref  mathscinet  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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