Moments of random multiplicative functions, III: A short review

2024/10/15 by Adam J. Harper, Harper, Adam J. · 5 citations
Decision Sciences · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2410.11523

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short review of recent progress on determining the order of magnitude of moments 𝔼|∑_{n ≤ x} f(n)|^2q of random multiplicative functions, and of closely related issues. We hope this can serve as a concise introduction to some of the ideas involved, for those who may not have too much background in the area.

Cited by

• Better than squareroot cancellation in number theory
• Central limit theorems for random multiplicative functions over function fields
• Helson's conjecture for smooth numbers
• On the limiting distribution of sums of random multiplicative functions
• A sharp almost sure upper bound for partial sums of random multiplicative functions

Related

• Moments of random multiplicative functions, I: Low moments, better than\n squareroot cancellation, and critical multiplicative chaos
• A note on Helson's conjecture on moments of random multiplicative functions
• Moments of random multiplicative functions over function fields
• On the limit distributions of some sums of a random multiplicative function
• Moments of random multiplicative functions and truncated characteristic polynomials