Restricted sum formula for finite and symmetric multiple zeta values

TL;DR

This paper extends the sum formula for finite and symmetric multiple zeta values, showing that under additional constraints on components, the sum still simplifies to a rational multiple of the Riemann zeta value analogue.

Contribution

It proves that the sum formula remains valid when additional component constraints are imposed, broadening the understanding of multiple zeta value relations.

Findings

Sum formula holds with components > 2

Sum formula holds with another component > 1

Values sum to a rational multiple of the Riemann zeta analogue

Abstract

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to a rational multiple of the analogue of the Riemann zeta value. We prove that the result remains true if we further demand that the component should be more than two or that another component should also be more than one.