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Moments of random multiplicative functions over function fields

Published online by Cambridge University Press:  08 August 2025

MAXIMILIAN C. E. HOFMANN
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, U.S.A. e-mail: maximilian.hofmann@stonybrook.edu
ANNEMILY HOGANSON
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, U.S.A. e-mail: aghoganson@wisc.edu
SIDDARTH MENON
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WB. e-mail: sm2884@cam.ac.uk
WILLIAM VERREAULT
Affiliation:
Department of Mathematics, University of Toronto, ON, M5S 2E4, Canada. e-mails: william.verreault@utoronto.ca, asif.zaman@utoronto.ca
ASIF ZAMAN
Affiliation:
Department of Mathematics, University of Toronto, ON, M5S 2E4, Canada. e-mails: william.verreault@utoronto.ca, asif.zaman@utoronto.ca

Abstract

Granville–Soundararajan, Harper–Nikeghbali–Radziwiłł 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.

Information

Type
Research Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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