Polynomial generalization of the regularization theorem for multiple zeta values

TL;DR

This paper generalizes the regularization theorem for multiple zeta values to polynomial forms, linking different regularizations and symmetric multiple zeta values, expanding the theoretical framework of multiple zeta value relations.

Contribution

The paper introduces a polynomial generalization of the regularization theorem, connecting various regularizations and symmetric multiple zeta values.

Findings

Generalized the regularization theorem to polynomial coefficients.

Established a connection between regularizations and symmetric multiple zeta values.

Expanded the theoretical understanding of multiple zeta value relations.

Abstract

Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We show that the regularization theorem can be generalized to polynomials whose coefficients are regularizations of multiple zeta values and that specialize to symmetric multiple zeta values defined by Kaneko and Zagier.