UNIVERSALITY OF ZETA-FUNCTIONS OF CUSP FORMS AND NON-TRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION-Reference-Cited by-同舟云学术

UNIVERSALITY OF ZETA-FUNCTIONS OF CUSP FORMS AND NON-TRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

Published:2021-01-18 Issue:1 Volume:26 Page:82-93
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Balčiūnas Aidas¹,Franckevič Violeta¹,Garbaliauskienė Virginija²,Macaitienė Renata³^ORCID,Rimkevičienė Audronė⁴

Affiliation:

1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania

2. Institute of Regional Development, Šiauliai University, P. Višinskio g. 25, LT-76351, Šiauliai, Lithuania

3. Institute of Regional Development, Šiauliai University, P. Višinskio g. 25, LT-76351 Šiauliai, Lithuania

4. Faculty of Business and Technologies, Šiauliai State College, Aušros al. 40, LT-76241 Šiauliai, Lithuania

Abstract

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

Reference16 articles.

1. JOINT DISCRETE APPROXIMATION OF A PAIR OF ANALYTIC FUNCTIONS BY PERIODIC ZETA-FUNCTIONS

2. P. Billingsley. Convergence of Probability Measures. Wiley, New York, 1968.

3. Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros

4. The Riemann hypothesis and universality of the Riemann zeta-function

5. Zeros of the Riemann zeta-function and its universality

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