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

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Limit theorems Stochastic processes

Published online by Cambridge University Press:  28 February 2022

DAKSH AGGARWAL ,
UNIQUE SUBEDI ,
WILLIAM VERREAULT ,
ASIF ZAMAN  and
CHENGHUI ZHENG
DAKSH AGGARWAL
Affiliation:
Department of Mathematics, Grinnell College, 1115 8th Ave # 3011, Grinnell, IA, USA, 50112 e-mail: aggarwal2@grinnell.edu
UNIQUE SUBEDI
Affiliation:
Department of Statistics, University of Michigan, 1085 University Ave, 323 West Hall, Ann Arbor, MI, USA, 48109 e-mail: subedi@umich.edu
WILLIAM VERREAULT
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, QC, G1V 0A6, Canada e-mail: william.verreault.2@ulaval.ca
ASIF ZAMAN
Affiliation:
Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, ON, Canada, M5S 2E4 e-mail: zaman@math.toronto.edu
CHENGHUI ZHENG
Affiliation:
Department of Statistics, University of Toronto, 100 St.George Street, Toronto, ON, Canada, M5S 3G3 e-mail: chenghui.zheng@mail.utoronto.ca
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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.

MSC classification

Primary: 11K65: Arithmetic functions
Secondary: 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 3 , November 2022 , pp. 715 - 726
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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