The $\boldsymbol{p}$-adic duality for the finite star-multiple polylogarithms

TL;DR

This paper establishes a p-adic duality theorem for finite star-multiple polylogarithms, extending Hoffman's duality for finite multiple zeta-star values, thus advancing the understanding of p-adic properties in multiple polylogarithms.

Contribution

It introduces a p-adic duality theorem for finite star-multiple polylogarithms, generalizing Hoffman's duality for finite multiple zeta-star values.

Findings

Proves the p-adic duality theorem for finite star-multiple polylogarithms.

Generalizes Hoffman's duality theorem to a p-adic setting.

Enhances the theoretical framework of p-adic multiple polylogarithms.

Abstract

We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.