Double shuffle relations and renormalization of multiple zeta values

TL;DR

This paper reviews recent advances in multiple zeta values, focusing on double shuffle relations, generalizations of classical formulas, and extending these relations to divergent cases using methods from quantum field theory and pseudodifferential calculus.

Contribution

It introduces methods from quantum field theory and pseudodifferential calculus to extend double shuffle relations to divergent multiple zeta values.

Findings

Summarizes double shuffle relations for convergent MZVs

Generalizes sum and decomposition formulas of Euler for MZVs

Extends double shuffle relations to divergent MZVs using novel methods

Abstract

In this paper we present some of the recent progresses in multiple zeta values (MZVs). We review the double shuffle relations for convergent MZVs and summarize generalizations of the sum formula and the decomposition formula of Euler for MZVs. We then discuss how to apply methods borrowed from renormalization in quantum field theory and from pseudodifferential calculus to partially extend the double shuffle relations to divergent MZVs.