Quadratic relations for a q-analogue of multiple zeta values

TL;DR

This paper establishes quadratic relations for a q-analogue of multiple zeta values, connecting them to classical relations as q approaches 1, and employs q-analogues of Newton series and duality formulas in the proof.

Contribution

It introduces quadratic relations for q-analogues of multiple zeta values, extending Kawashima's relations to the q-setting and utilizing novel q-analogue techniques.

Findings

qMZV's satisfy Kawashima's linear relations

Quadratic relations generalize classical multiple zeta value relations

Proof uses q-analogues of Newton series and duality formulas

Abstract

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation contained in Kawashima's relation. In the proof we make use of a q-analogue of Newton series and Bradley's duality formula for finite multiple harmonic q-series.