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ON A CERTAIN CONVOLUTION OF POLYLOGARITHMS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  07 February 2012

HIROFUMI TSUMURA
HIROFUMI TSUMURA*
Affiliation:
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan (email: tsumura@tmu.ac.jp)
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Abstract

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In this paper, we consider certain double series analogous to Tornheim’s double series and real analytic Eisenstein series. By computing double integrals in two ways, we express the double series as a sum of products of polylogarithms. The technique generalises one given by Kanemitsu, Tanigawa and Yoshimoto. Evaluating the double series at particular points gives new evaluations for certain double series in terms of values of the Riemann zeta function and the dilogarithm which are analogues of formulas of Mordell and Goncharov.

Keywords

polylogarithmsRiemann zeta-functionreal analytic Eisenstein series

MSC classification

Secondary: 11M41: Other Dirichlet series and zeta functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 461 - 472
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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