On multiple zeta values of extremal height

TL;DR

This paper presents new identities and formulas for multiple zeta values, focusing on those of extremal heights, including explicit, regularized, and sum formulas for specific height cases.

Contribution

It introduces three novel identities involving multiple zeta values of height one and maximal height, expanding understanding of their structure and relationships.

Findings

Explicit formula for height-one multiple zeta values

Regularized sum formula for these values

Sum formula for multiple zeta values of maximal height

Abstract

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal height.