A note on derivation relations for multiple zeta values and finite multiple zeta values

TL;DR

This paper explores derivation relations for multiple zeta values and finite multiple zeta values, establishing their equivalence to Ohno type relations and providing multiple proofs for these relations.

Contribution

It demonstrates the equivalence of derivation relations to Ohno type relations and offers new proofs, deepening understanding of these mathematical structures.

Findings

Derivation relations are equivalent to Ohno type relations.

Multiple proofs of the derivation relations are provided.

The results unify different perspectives on multiple zeta values.

Abstract

The derivation relation is a well known relation among multiple zeta values, which was first obtained by Ihara, Kaneko and Zagier. The analogous formula for finite multiple zeta values, which we call the derivation relation for finite multiple zeta values, was conjectured by the third author and proved by the second author. In this paper, we show these two kinds of derivation relations are respectively equivalent to the Ohno type relations for multiple zeta values and finite multiple zeta values. We also reprove these derivation relations in several different ways.