Involution on a quotient space of multiple zeta values in positive characteristic

TL;DR

This paper introduces new multiple zeta values in positive characteristic and constructs an involution on a quotient space, revealing novel symmetries and properties of these special functions.

Contribution

It presents the first construction of an involution on a quotient space of multiple zeta values in positive characteristic using Carlitz multiple dagger polylogarithms.

Findings

Defined multiple zeta dagger values and Carlitz multiple dagger polylogarithms.

Constructed a non-trivial involution on a quotient space of multiple zeta values.

Explored properties and symmetries of these new special values.

Abstract

In this paper, we introduce multiple zeta dagger values and special values of Carlitz multiple dagger polylogarithms, and study their properties. In particular, using these values, we construct a non-trivial involution on a certain quotient space of multiple zeta values in positive characteristic.