An explicit parity theorem for multiple polylogarithms

Ryota Umezawa

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arXiv · 2508.02040

An explicit parity theorem for multiple polylogarithms

Ryota Umezawa

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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.

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Ryota Umezawa. 2025-08-04. An explicit parity theorem for multiple polylogarithms. https://arxiv.org/abs/2508.02040

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