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VOL. 63 | 2012 Geometric interpretation of double shuffle relation for multiple $L$-values
Hidekazu Furusho

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

## Abstract

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.

## Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1321.11089
MathSciNet: MR3051243

Digital Object Identifier: 10.2969/aspm/06310163

Subjects:
Primary: 11M32
Secondary: 11G55