The evaluation of character Euler double sums

被引：45

作者：

Borwein, J. M. ^{[2
]}

Zucker, I. J. ^{[1
]}

Boersma, J. ^{[3
]}

机构：

[1] Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England

[2] Dalhousie Univ, Fac Comp Sci, Halifax, NS B3H 3J5, Canada

[3] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

来源：

RAMANUJAN JOURNAL | 2008年 / 15卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Euler sums; Dirichlet characters; Riemann zeta function;

D O I：

10.1007/s11139-007-9083-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Euler considered sums of the form [GRAPHICS] Here natural generalizations of these sums namely [GRAPHICS] are investigated, where chi(p) and chi(q) are characters, and s and t are positive integers. The cases when p and q are either 1, 2a, 2b or -4 are examined in detail, and closed-form expressions are found for t = 1 and general s in terms of the Riemann zeta function and the Catalan zeta function-the Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) - 7(-s) + center dot center dot center dot. Some results for arbitrary p and q are obtained as well.

引用

页码：377 / 405

页数：29

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