Renormalisation of q-regularised multiple zeta values

TL;DR

This paper introduces a renormalisation method for a specific family of q-analogues of multiple zeta values, extending their domain and preserving algebraic structures using Hopf algebra techniques.

Contribution

It develops a novel renormalisation approach for q-multiple zeta values that maintains the quasi-shuffle product structure through Hopf algebraic Birkhoff factorisation.

Findings

Extended q-multiple zeta values to negative integers

Maintained quasi-shuffle algebraic structure after renormalisation

Provided a systematic Hopf algebraic framework for renormalisation

Abstract

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the quasi-shuffle product are obtained using an Hopf algebraic Birkhoff factorisation together with minimal subtraction.