On the sum and the regularized products of some Dirichlet series

被引：0

作者：

Hajli, Mounir ^{[1
]}

机构：

[1] Westlake Univ, Sch Sci, Hangzhou 310024, Peoples R China

来源：

RAMANUJAN JOURNAL | 2024年 / 65卷 / 04期

关键词：

Lerch's formula; Hurwitz zeta function; Zeta regularized product; ANALYTIC TORSION;

D O I：

10.1007/s11139-023-00796-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, using zeta functions, we evaluate the regularized products of some Dirichlet series generalizing Lerch's formula and we show that they are multiplicative. As an application, we determine the sum of some Dirichlet series generalizing Euler's formula on the sum of the reciprocal of squares.

引用

页码：1799 / 1812

页数：14

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