Structural identities for generalized multiple zeta values

TL;DR

This paper introduces a framework dividing multiple zeta value identities into structural and specific types, enabling systematic analysis and closed-form evaluations, and interprets these values as moments of random variables.

Contribution

It systematically investigates structural identities for generalized multiple zeta functions using symmetric functions and combines them with specific identities for explicit evaluations.

Findings

Structural identities hold for any generalized multiple zeta function.

Closed-form expressions for certain multiple zeta values are derived.

Generalized multiple zeta values are interpreted as moments of random variables.

Abstract

There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function, and we systematically investigate them through symmetric functions. Specific identities are only valid for a specific zeta function, and we show how these can be used in conjunction with structural identities to find closed form multiple zeta values. This allows us to interpret generalized multiple zeta values as the moments of a random variable, which we characterize in certain cases. We also evaluate certain multiple Bessel zeta values and multiple Hurwitz zeta values.