English

An explicit parity theorem for multiple polylogarithms

Number Theory 2025-08-05 v1

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.

Cite

@article{arxiv.2508.02040,
  title  = {An explicit parity theorem for multiple polylogarithms},
  author = {Ryota Umezawa},
  journal= {arXiv preprint arXiv:2508.02040},
  year   = {2025}
}

Comments

18 pages

R2 v1 2026-07-01T04:32:24.167Z