Relationship between renormalized values of shuffle type and of harmonic type of multiple zeta functions

TL;DR

This paper resolves a problem posed by Singer by comparing the renormalized values of shuffle type and harmonic type multiple zeta functions, clarifying their relationship.

Contribution

It provides a definitive comparison between two different renormalization approaches for multiple zeta functions, addressing a previously open problem.

Findings

Established the relationship between shuffle and harmonic renormalized values.

Resolved Singer's comparison problem for multiple zeta functions.

Clarified the structure of renormalized multiple zeta values.

Abstract

In this paper, we settle the problem posed by Singer which is on a comparison problem between the renormalized values of shuffle type and of harmonic type of multiple zeta functions.