Moments of random multiplicative functions over function fields

TL;DR

This paper extends the study of moments of random multiplicative functions to the setting of function fields, providing asymptotic formulas and exact results for even moments in large field and degree limits.

Contribution

It introduces new asymptotic formulas for moments of Steinhaus random multiplicative functions over function fields, building on prior integer-based results.

Findings

Asymptotic expressions for all even moments in large field and degree limits

Exact formula for the fourth moment over function fields

Analytic and combinatorial methods applied to function field setting

Abstract

Granville-Soundararajan, Harper-Nikeghbali-Radziwill, and Heap-Lindqvist independently established an asymptotic for the even natural moments of partial sums of random multiplicative functions defined over integers. Building on these works, we study the even natural moments of partial sums of Steinhaus random multiplicative functions defined over function fields. Using a combination of analytic arguments and combinatorial arguments, we obtain asymptotic expressions for all the even natural moments in the large field limit and large degree limit, as well as an exact expression for the fourth moment.