An Explicit Expression for MZVs in Terms of Symmetric MZVs

Katsumi Kina

An Explicit Expression for MZVs in Terms of Symmetric MZVs

Number Theory 2026-07-07 v1

Authors: Katsumi Kina

Abstract

We provide a simpler proof of the fact, originally proved by Seidai Yasuda, that symmetric multiple zeta values generate the entire space of multiple zeta values. Furthermore, based on this argument, we present an algorithm for expressing multiple zeta values in terms of symmetric multiple zeta values and products of multiple zeta values. Moreover, we give some results on symmetric and finite multiple zeta values of depth three.

Keywords

multiple zeta values symmetric multiple zeta values finite multiple zeta values explicit expression algorithm

Cite

@article{arxiv.2607.05795,
  title  = {An Explicit Expression for MZVs in Terms of Symmetric MZVs},
  author = {Katsumi Kina},
  journal= {arXiv preprint arXiv:2607.05795},
  year   = {2026}
}