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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Mordell-Tornheim zeta values
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by Hirofumi Tsumura PDF
Proc. Amer. Math. Soc. 133 (2005), 2387-2393 Request permission


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
  • Email:,
  • 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
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2387-2393
  • MSC (2000): Primary 40B05; Secondary 11M06, 30B99, 33E20, 40A05
  • DOI:
  • MathSciNet review: 2138881