On the quasi-derivation relation for multiple zeta values

TL;DR

This paper proves Kaneko's conjecture on an extended derivation relation for multiple zeta values by linking it to Kawashima's relations and explores algebraic properties of a quasi-derivation operator inspired by Hopf algebra theory.

Contribution

It provides a proof of Kaneko's conjecture and analyzes the algebraic structure of the quasi-derivation operator in the context of multiple zeta values.

Findings

Proof of Kaneko's conjecture established.

Reduction of the conjecture to Kawashima's relations.

Analysis of algebraic properties of the quasi-derivation operator.

Abstract

Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relation for multiple zeta values. The goal of the present paper is to present a proof of this conjecture by reducing it to a class of relations for multiple zeta values studied by Kawashima. In addition, some algebraic aspects of the quasi-derivation operator $\partial_n^{(c)}$ on $\mathbb{Q}< x,y>$, which was defined by modeling a Hopf algebra developed by Connes and Moscovici, will be presented.