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A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions
Version 1
: Received: 4 June 2024 / Approved: 5 June 2024 / Online: 6 June 2024 (02:54:33 CEST)
A peer-reviewed article of this Preprint also exists.
Gerges, H.; Laurinčikas, A.; Macaitienė, R. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions. Mathematics 2024, 12, 1922. Gerges, H.; Laurinčikas, A.; Macaitienė, R. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions. Mathematics 2024, 12, 1922.
Abstract
In the paper, we prove a joint limit theorem in terms of weak convergence of probability measures on $\mathbb{C}^2$ 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 parameter α are required. The theorem obtained extends and generalizes Bohr-Jessen’s results characterising asymptotic behaviour of the Riemann zeta-function.
Keywords
dirichlet L-function; epstein zeta-function; hurwitz zeta-function; limit theorem; probability haar measure; weak convergence
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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