Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Galois–Teichmüller Theory and Arithmetic Geometry, H. Nakamura, F. Pop, L. Schneps and A. Tamagawa, eds. (Tokyo: Mathematical Society of Japan, 2012), 163 - 187
Geometric interpretation of double shuffle relation for multiple $L$-values
This paper gives a geometric interpretation of the generalized (including the regularization relation) double shuffle relation for multiple $L$-values. Precisely it is proved that Enriquez' mixed pentagon equation implies the relations. As a corollary, an embedding from his cyclotomic analogue of the Grothendieck–Teichmüller group into Racinet's cyclotomic double shuffle group is obtained. It cyclotomically extends the result of our previous paper [F3] and the project of Deligne and Terasoma which are the special case $N=1$ of our result.
Received: 2 April 2011
Revised: 24 February 2012
First available in Project Euclid: 24 October 2018
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Furusho, Hidekazu. Geometric interpretation of double shuffle relation for multiple $L$-values. Galois–Teichmüller Theory and Arithmetic Geometry, 163--187, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06310163. https://projecteuclid.org/euclid.aspm/1540417818