Anderson-Thakur polynomials and multizeta values in positive characteristic

TL;DR

This paper studies Anderson-Thakur polynomials and confirms conjectured zeta-like families of multizeta values in positive characteristic, providing explicit formulas and advancing understanding in this area.

Contribution

It offers a transparent formula for specific Anderson-Thakur polynomials and verifies conjectured zeta-like families of multizeta values in positive characteristic.

Findings

Derived explicit formulas for Anderson-Thakur polynomials.

Confirmed conjectured zeta-like families of multizeta values.

Enhanced understanding of multizeta values in positive characteristic.

Abstract

Multizeta values in positive characteristic were first introduced and studied by Thakur. He and Lara Rodr\'{\i}guez discovered and conjectured certain zeta-like families. Kuan and Lin stated more conjectures about zeta-like multizeta values. In the present paper we study and give a transparent formula for certain Anderson-Thakur polynomials. Besides, we confirm the conjectured zeta-like families.