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Article

A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
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Mathematics 2024, 12(13), 1922; https://doi.org/10.3390/math12131922
Submission received: 3 June 2024 / Revised: 14 June 2024 / Accepted: 18 June 2024 / Published: 21 June 2024

Abstract

In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C2 defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and the parameter α are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function.
Keywords: Dirichlet L-function; Epstein zeta-function; Hurwitz zeta-function; limit theorem; Haar probability measure; weak convergence Dirichlet L-function; Epstein zeta-function; Hurwitz zeta-function; limit theorem; Haar probability measure; weak convergence

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MDPI and ACS Style

Gerges, H.; Laurinčikas, A.; Macaitienė, R. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions. Mathematics 2024, 12, 1922. https://doi.org/10.3390/math12131922

AMA Style

Gerges H, Laurinčikas A, Macaitienė R. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions. Mathematics. 2024; 12(13):1922. https://doi.org/10.3390/math12131922

Chicago/Turabian Style

Gerges, Hany, Antanas Laurinčikas, and Renata Macaitienė. 2024. "A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions" Mathematics 12, no. 13: 1922. https://doi.org/10.3390/math12131922

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