A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

被引：0

作者：

Gerges, Hany ^{[1
]}

Laurincikas, Antanas ^{[1
]}

Macaitiene, Renata ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math, Fac Math & Informat, Naugarduko Str 24, LT-03225 Vilnius, Lithuania

来源：

MATHEMATICS | 2024年 / 12卷 / 13期

关键词：

Dirichlet L-function; Epstein zeta-function; Hurwitz zeta-function; limit theorem; Haar probability measure; weak convergence;

D O I：

10.3390/math12131922

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 zeta(s;Q) and Hurwitz zeta(s,alpha) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and the parameter alpha are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function.

引用

页数：15

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