Title A joint limit theorem for Epstein and Hurwitz zeta-functions /
Authors Gerges, Hany ; Laurinčikas, Antanas ; Macaitienė, Renata
DOI 10.3390/math12131922
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Is Part of Mathematics.. Basel : MDPI. 2024, vol. 12, iss. 13, art. no. 1922, p. [1-15].. ISSN 2227-7390
Keywords [eng] Dirichlet L-function ; Epstein zeta-function ; Hurwitz zeta-function ; limit theorem ; Haar probability measure ; weak convergence
Abstract [eng] In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on 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 the parameter α are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function.
Published Basel : MDPI
Type Journal article
Language English
Publication date 2024
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