Title |
A joint limit theorem for Epstein and Hurwitz zeta-functions / |
Authors |
Gerges, Hany ; Laurinčikas, Antanas ; Macaitienė, Renata |
DOI |
10.3390/math12131922 |
Full Text |
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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 |
CC license |
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