On Log-Algebraic Identities for Anderson t-modules and Characteristic p Multiple Zeta Values

TL;DR

This paper introduces a new approach using Stark units to refine log-algebraic identities for Anderson t-modules, leading to generalized theorems on multiple zeta values in characteristic p and their logarithmic interpretations.

Contribution

It provides a novel method to refine log-algebraic identities and generalizes existing theorems on multiple zeta values and their interpretations in characteristic p.

Findings

Refined log-algebraic identities for Anderson t-modules.

Generalized Chang's theorem on MZV logarithmic interpretations.

Unified approach for MZV and v-adic MZV logarithmic interpretations.

Abstract

Based on the notion of Stark units we present a new approach that obtains refinements of log-algebraic identities for Anderson t-modules. As a consequence, we establish a generalization of Chang's theorem on logarithmic interpretations for special characteristic p multiple zeta values (MZV's) and recover many earlier results in this direction. Further, we devise a direct and conceptual way to get logarithmic interpretations for both MZV's and v-adic MZV's. This generalizes completely the work of Anderson and Thakur for Carlitz zeta values.