The evaluation of character Euler double sums

Title: The evaluation of character Euler double sums
Creator: Borwein, J. M.; Zucker, I. J.; Boersma, J.
Relation: The Ramanujan Journal Vol. 15, Issue 3, p. 377-405
Publisher Link: http://dx.doi.org/10.1007/s11139-007-9083-z
Publisher: Springer
Resource Type: journal article
Date: 2008
Description: Euler considered sums of the form [formula unable to be reproduced here]. Here natural generalizations of these sums namely [formula unable to be reproduced here], are investigated, where χ p and χ 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 +⋅⋅⋅. Some results for arbitrary p and q are obtained as well.
Subject: euler sums; dirichlet characters; riemann zeta function
Identifier: http://hdl.handle.net/1959.13/928076
Identifier: uon:10334
Identifier: ISSN:1382-4090
Language: eng
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