Moments of random multiplicative functions over function fields

Maximilian C. E. Hofmann, Annemily Hoganson, Siddarth Menon, William Verreault, Asif Zaman

Published 2024-08-15Version 1

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.