Linear independence of monomials of multizeta values in positive characteristic

TL;DR

This paper advances the understanding of algebraic independence of multizeta values and Carlitz polylogarithms in positive characteristic, proving key conjectures in transcendence theory.

Contribution

It proves an analogue of Goncharov's conjecture for multizeta values and extends results to Carlitz multiple polylogarithms at algebraic points.

Findings

Proved an analogue of Goncharov's conjecture for multizeta values

Established algebraic independence results for Carlitz polylogarithms

Enhanced transcendence theory in positive characteristic

Abstract

In this paper, we study transcendence theory for Thakur multizeta values in positive characteristic. We prove an analogue of the strong form of Goncharov's conjecture. We also establish the same result for Carlitz multiple polylogarithms at nontrivial algebraic points.