Transfer group for renormalized multiple zeta values

TL;DR

This paper develops a comprehensive transfer group framework for renormalizing multiple zeta values at all integer arguments, clarifying relations among various recent renormalization methods.

Contribution

It introduces a transfer group approach that systematically characterizes all quasi-shuffle compatible renormalizations of multiple zeta values at arbitrary arguments.

Findings

All solutions to the renormalization problem are described.

Clarifies the relations between different recent renormalizations.

Provides a unified framework for understanding multiple zeta value renormalizations.

Abstract

We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at non-positive values appearing in the recent literature.