On Thakur's basis conjecture for multiple zeta values in positive characteristic

TL;DR

This paper proves Thakur's basis conjecture for multiple zeta values over function fields in positive characteristic, establishing a foundational basis and confirming related dimension conjectures in this mathematical setting.

Contribution

It provides the first proof of Thakur's basis conjecture and confirms Todd's dimension conjecture for MZV's in positive characteristic.

Findings

Proof of Thakur's basis conjecture

Confirmation of Todd's dimension conjecture

Advancement in understanding MZV's in positive characteristic

Abstract

In this paper, we study multiple zeta values (abbreviated as MZV's) over function fields in positive characteristic. Our main result is to prove Thakur's basis conjecture, which plays the analogue of Hoffman's basis conjecture for real MZV's. As a consequence, we derive Todd's dimension conjecture, which is the analogue of Zagier's dimension conjecture for classical real MZV's.