1. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions
- Author
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Hany Gerges, Antanas Laurinčikas, and Renata Macaitienė
- Subjects
Dirichlet L-function ,Epstein zeta-function ,Hurwitz zeta-function ,limit theorem ,Haar probability measure ,weak convergence ,Mathematics ,QA1-939 - 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.
- Published
- 2024
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