On a generalization of restricted sum formula for multiple zeta values and finite multiple zeta values

TL;DR

This paper introduces a new linear relation for multiple zeta values, generalizing existing sum formulas, and extends the result to finite multiple zeta values, enhancing understanding of their algebraic structure.

Contribution

It provides a novel generalization of the restricted sum formula for multiple zeta values and establishes an analogous relation for finite multiple zeta values.

Findings

New linear relation for multiple zeta values

Generalization of the restricted sum formula

Analogous relation for finite multiple zeta values

Abstract

We prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.