A parameterized generalization of the sum formula for quadruple zeta values

TL;DR

This paper introduces a parameterized generalization of the sum formula for quadruple zeta values, revealing new invariance properties and deriving weighted sum formulas that encompass known results.

Contribution

It presents a novel four-parameter generalization of the quadruple zeta sum formula, highlighting symmetry and deriving weighted formulas from special parameter choices.

Findings

Invariance under a cyclic group of order four

Derivation of weighted sum formulas from special parameters

Unification of known results within the new framework

Abstract

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also obtain weighted sum formulas for quadruple zeta values, which contain some known results.