Shuffle product of finite multiple polylogarithms

Masataka Ono, Shuji Yamamoto

Published 2015-02-24Version 1

In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zaiger and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition due to Komori-Matsumoto-Tsumura. As a corollary, we give an algebraic interpretation of our shuffle product.