The autocorrelation of the M\"obius function and Chowla's conjecture for the rational function field in characteristic 2

TL;DR

This paper proves a version of Chowla's conjecture regarding the autocorrelation of the M"obius function within the context of function fields over large finite fields of characteristic 2.

Contribution

It establishes a function field analogue of Chowla's conjecture specifically for characteristic 2, expanding understanding of M"obius function behavior in this setting.

Findings

Proves a function field version of Chowla's conjecture in characteristic 2.

Demonstrates autocorrelation properties of the M"obius function in this context.

Extends classical number theory results to function fields in characteristic 2.

Abstract

We prove a function field version of Chowla's conjecture on the autocorrelation of the M\"obius function in the limit of a large finite field of characteristic 2.