Compositio Mathematica

Derivation and double shuffle relations for multiple zeta values

Kentaro Ihara a1, Masanobu Kaneko a2 and Don Zagier a3
a1 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
a2 Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
a3 Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany and Collège de France, 3 rue d'Ulm, F-75005 Paris, France

Article author query
ihara k   [Google Scholar] 
kaneko m   [Google Scholar] 
zagier d   [Google Scholar] 


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.

(Published Online March 13 2006)
(Received September 22 2004)
(Accepted April 18 2005)

Key Words: multiple zeta value; double shuffle relation; regularization; derivation.

Maths Classification

11M41 (primary); 11M06 (secondary).