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Derivation and double shuffle relations for multiple zeta values

Published online by Cambridge University Press:  13 March 2006

Kentaro Ihara ,
Masanobu Kaneko  and
Don Zagier
Kentaro Ihara
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japank-ihara@math.nagoya-u.ac.jp
Masanobu Kaneko
Affiliation:
Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japanmkaneko@math.kyushu-u.ac.jp
Don Zagier
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany and Collège de France, 3 rue d'Ulm, F-75005 Paris, Francezagier@mpim-bonn.mpg.de
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Abstract

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Derivation and extended double shuffle (EDS) relations for multiple zeta values (MZVs) are proved. Related algebraic structures of MZVs, as well as a ‘linearized’ version of EDS relations are also studied.

Keywords

multiple zeta valuedouble shuffle relationregularizationderivation11M41 (primary)11M06 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 2 , March 2006 , pp. 307 - 338
Copyright
Foundation Compositio Mathematica 2006