On the Mishou Theorem for Zeta-Functions with Periodic Coefficients-Reference-Cited by-同舟云学术

On the Mishou Theorem for Zeta-Functions with Periodic Coefficients

Published:2023-04-25 Issue:9 Volume:11 Page:2042
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Balčiūnas Aidas¹^ORCID,Jasas Mindaugas¹,Macaitienė Renata²^ORCID,Šiaučiūnas Darius²^ORCID

Affiliation:

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

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

Abstract

Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet series ζnT(s;a) and ζnT(s,α;b) involving the sequences a and b is considered. Here, nT→∞ and nT≪T2 as T→∞. The coefficients of these series tend to am and bm, respectively. It is proved that the set of the above shifts in the interval [0,T] has a positive density. This generalizes and extends the Mishou joint universality theorem for the Riemann and Hurwitz zeta-functions.

Funder

Research Council of Lithuania

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/9/2042/pdf

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