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On Mordell-Tornheim zeta values
Author(s):
Hirofumi
Tsumura
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2387-2393.
MSC (2000):
Primary 40B05;
Secondary 11M06, 30B99, 33E20, 40A05
Posted:
March 21, 2005
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Abstract:
We prove that the Mordell-Tornheim zeta value of depth  can be expressed as a rational linear combination of products of the Mordell-Tornheim zeta values of lower depth than  when  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:
tsumura@tmca.ac.jp, tsumura@comp.metro-u.ac.jp
DOI:
10.1090/S0002-9939-05-08132-3
PII:
S 0002-9939(05)08132-3
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
Posted:
March 21, 2005
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2005,
American Mathematical Society
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