Iterated integrals and relations of multiple polylogarithms

TL;DR

This paper explores the structure of multiple polylogarithms through iterated integrals, revealing new relations such as the five-term relation for the dilogarithm, and connects these to the harmonic product of multiple zeta values.

Contribution

It introduces new relations among multiple polylogarithms, including a novel five-term relation for the dilogarithm, expanding understanding of their algebraic structure.

Findings

New five-term relation for the dilogarithm

Connections between iterated integrals and multiple zeta values

Enhanced understanding of the algebraic relations of polylogarithms

Abstract

This is a summary for the authors' article "The formal KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple zeta values" (prerint (2009) arXiv:0910.0718), including a new result on the five term relation for the dilogarithm. This note will appear in the RIMS K\^oky\^uroku for the conference on "Representation Theory and Combinatorics" held at Hokkaido University from August 25th to 28th, 2009.