Sums of random multiplicative functions over function fields with few irreducible factors

TL;DR

This paper proves a normal distribution approximation for sums of random multiplicative functions over function fields, specifically when polynomials have few irreducible factors, extending Harper's results from integers to function fields.

Contribution

It introduces a normal approximation result for partial sums of random Rademacher multiplicative functions over function fields with limited irreducible factors, a novel extension of existing integer-based work.

Findings

Normal approximation established for sums over function fields

Applicable when polynomials have few irreducible factors

Extends Harper's results from integers to function fields

Abstract

We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreducible factors of the polynomials is small enough. This parallels work of Harper for random Rademacher multiplicative functions over the integers.