Relations between multizeta values in characteristic p

TL;DR

This paper investigates algebraic relations among multizeta values in function fields, proving main conjectures and providing recursive formulas for expressing products of zeta values as sums of multizeta values.

Contribution

It proves the main conjecture about relations between multizeta values and generalizes recursive formulas for all q, advancing understanding in function field multizeta theory.

Findings

Proved the main conjecture relating multizeta values.

Established closed formulas for products of zeta values.

Provided recursive recipes for expressing products as sums.

Abstract

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta values can be described as the sum of multizetas was given by Thakur. The recursion part of this recipe was generalized by the author. In this paper, the main conjecture formulated by the author, as well as some conjectures of Thakur are proved. Moreover, for general q, we prove closed formulas as well as a recursive recipe to express \zeta(a)\zeta(b) as a sum of multizeta values.