On lower bounds of the dimensions of multizeta values in positive characteristic

TL;DR

This paper investigates the linear independence of multizeta values and related special values in positive characteristic, establishing lower bounds on the dimension of their span for fixed weight and depth.

Contribution

It provides new lower bounds on the dimensions of spaces generated by multizeta values in positive characteristic, extending understanding of their linear independence.

Findings

Established linearly independent sets of special values at algebraic points.

Derived lower bounds for the dimension of spaces of multizeta values with fixed weight and depth.

Enhanced the theoretical framework for understanding multizeta values in positive characteristic.

Abstract

In this paper, we study the linear independence of special values, including the positive characteristic analogue of multizeta values, alternating multizeta values and multiple polylogarithms, at algebraic points. Consequently, we establish linearly independent sets of these values with the same weight indices and a lower bound on the dimension of the space generated by depth r > 2 multizeta values of the same weight in positive characteristic.