On Hoffman's conjectural identity

TL;DR

This paper proves Hoffman's conjectural identity relating multiple zeta values using identities among iterated integrals on a punctured projective line.

Contribution

It provides a proof of Hoffman's conjecture on a specific multiple zeta value identity through novel integral identities.

Findings

Confirmed Hoffman's conjectural identity.

Established new identities among iterated integrals.

Enhanced understanding of multiple zeta value relations.

Abstract

In this paper, we shall prove the equality \[ \zeta(3,\{2\}^{n},1,2)=\zeta(\{2\}^{n+3})+2\zeta(3,3,\{2\}^{n}) \] conjectured by Hoffman using certain identities among iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty,z\}$.