Shuffle product of finite multiple polylogarithms

Abstract

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.

13 pages

References in corpus (2)

• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation