On a Conjecture of Gezmis and Pellarin

TL;DR

This paper investigates the structure of a specific map between trivial and Thakur's multiple zeta values, providing a proof regarding its injectivity and clarifying the relations among these special values.

Contribution

It determines the kernel of the map from trivial to Thakur's multiple zeta values, resolving a conjecture about its injectivity.

Findings

Kernel of the map is explicitly characterized

Confirmed the injectivity conjecture for the map

Clarified relations among multiple zeta values

Abstract

In 2022, Gezmis and Pellarin introduced and studied the concept of trivial multiple zeta values, along with a map from the vector space spanned by these values to the vector space spanned by Thakur's multiple zeta values. Their construction allows us to generate some linear relations among the latter values using the former. In our work, we determine the structure of the kernel of the aforementioned map. As a consequence, we give an answer to a conjecture proposed by Gezmis and Pellarin regarding the injectivity of this specific map.