Hostname: page-component-5b777bbd6c-rbv74 Total loading time: 0 Render date: 2025-06-18T17:55:05.448Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost sure upper bound for a model problem for multiplicative chaos in number theory

Part of: Multiplicative number theory Limit theorems Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  13 May 2025

RACHID CAICH
RACHID CAICH*
Affiliation:
Université Paris Cité, Sorbonne Université CNRS, Institut de Mathématiques de Jussieu- Paris Rive Gauche, F-75013 Paris, France. e-mail: rachid.caich.ing@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result of the author concerning an almost sure upper bound of random multiplicative functions. Having a simpler quantity allows us to make the proof more accessible.

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions 11K99: None of the above, but in this section
Secondary: 60F15: Strong theorems
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 179 , Issue 1 , July 2025 , pp. 29 - 44
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Caich, R.. Almost sure upper bound for random multiplicative functions. Preprint ArXiv:2304.00943 (2023).Google Scholar
Gerspach, M.. Almost sure lower bound for a model problem for multiplicative chaos in number theory. Mathematika 68 (2022), 1331–1363.CrossRefGoogle Scholar
Gut, A.. Probability: a Graduate Course . Internat. Ser. Monogr. Phys. vol. 75 (Springer, New York, 2005).Google Scholar
Harper, A. J.. Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos. Forum Math. Pi 8 (2020), 95pp.CrossRefGoogle Scholar
Harper, A. J.. Almost sure large fluctuations of random multiplicative functions. Internat. Math. Res. Not. 2023 (2021), 2095–2138.CrossRefGoogle Scholar
Lau, Y.-K., Tenenbaum, G. and Wu, J.. On mean values of random multiplicative functions. Proc. Amer. Math. Soc. 141 (2013), 409–420.CrossRefGoogle Scholar
Soundararajan, K.. and Zaman, A.. A model problem for multiplicative chaos in number theory. Enseign. Math. 68 (2021), 307–340.CrossRefGoogle Scholar