On multiple zeta values and finite multiple zeta values of maximal height

TL;DR

This paper provides an alternative proof for the explicit formula of height-one multiple zeta values and extends the result to finite multiple zeta values, enhancing understanding of their structure.

Contribution

It offers a new proof of known formulas and generalizes these results to finite multiple zeta values, contributing to the theoretical framework of multiple zeta values.

Findings

Alternative proof of the explicit formula for height-one multiple zeta values

Generalization of the formula to finite multiple zeta values

Enhanced understanding of the structure of multiple zeta values

Abstract

An explicit formula for the height-one multiple zeta values was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values.