The autocorrelation of the Mobius function and Chowla's conjecture for the rational function field

TL;DR

This paper proves a function field analogue of Chowla's conjecture, demonstrating the autocorrelation properties of the Mobius function over large finite fields, advancing understanding in number theory and finite field analysis.

Contribution

It establishes a new result by proving Chowla's conjecture in the context of function fields over large finite fields, which was previously unresolved.

Findings

Proves a function field version of Chowla's conjecture.

Shows autocorrelation properties of the Mobius function in finite fields.

Extends number theory results to the setting of function fields.

Abstract

We prove a function field version of Chowla's conjecture on the autocorrelation of the Mobius function in the limit of a large finite field.