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On Mordell-Tornheim zeta values

Author: Hirofumi Tsumura
Journal: Proc. Amer. Math. Soc. 133 (2005), 2387-2393
MSC (2000): Primary 40B05; Secondary 11M06, 30B99, 33E20, 40A05
Published electronically: March 21, 2005
MathSciNet review: 2138881
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Mordell-Tornheim zeta value of depth $r$ can be expressed as a rational linear combination of products of the Mordell-Tornheim zeta values of lower depth than $r$ when $r$ and its weight are of different parity.

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Additional Information

Hirofumi Tsumura
Affiliation: Department of Management Informatics, Tokyo Metropolitan College, Akishima, Tokyo 196-8540, Japan
Address at time of publication: Department of Mathematics, Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan

Keywords: Tornheim's double series, multiple zeta values, Riemann's zeta function, uniformly convergent series
Received by editor(s): July 7, 2003
Received by editor(s) in revised form: March 20, 2004
Published electronically: March 21, 2005
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2005 American Mathematical Society