Derivations on the algebra of multiple harmonic q-series and their applications

TL;DR

This paper develops derivations on the algebra of multiple harmonic q-series, revealing new linear relations and extending known results for q-analogues of multiple zeta values, including relations at roots of unity.

Contribution

It introduces derivations on the algebra of multiple harmonic q-series, generating new relations and extending existing q-analogue zeta value relations.

Findings

Derivations generate linear relations among q-series.

Contains derivation relations for q-analogue multiple zeta values.

Obtains Ohno-type relations at roots of unity.

Abstract

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a byproduct we obtain Ohno-type relations for finite multiple harmonic q-series at a root of unity.