The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2

Abstract

We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field of characteristic 2, extending previous work in odd characteristic.

Keywords: Berlekamp's discriminant; Chowla's conjecture; Möbius correlations; square independence.