An explicit parity theorem for multiple polylogarithms

TL;DR

This paper provides an explicit formula for the parity theorem of multiple polylogarithms, extending previous results and offering a constructive approach inspired by recent work on multiple zeta values.

Contribution

It introduces a new explicit formula for the parity theorem of multiple polylogarithms, advancing the understanding of their algebraic structure.

Findings

Derived an explicit parity formula for multiple polylogarithms

Extended the parity theorem beyond previous non-explicit proofs

Provides a constructive approach inspired by multiple zeta values

Abstract

In 2017, E. Panzer proved the parity theorem for multiple polylogarithms. While his proof is simple and constructive, it does not yield a general explicit formula. Inspired by M. Hirose's recent work on the parity theorem for multiple zeta values, this paper presents an explicit formula for the parity theorem for multiple polylogarithms.