Moments of random multiplicative functions over function fields
Number Theory
2025-10-08 v1 Probability
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.
Keywords
Cite
@article{arxiv.2408.08309,
title = {Moments of random multiplicative functions over function fields},
author = {Maximilian C. E. Hofmann and Annemily Hoganson and Siddarth Menon and William Verreault and Asif Zaman},
journal= {arXiv preprint arXiv:2408.08309},
year = {2025}
}
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32 pages