Better than square-root cancellation for random multiplicative functions

2023/03/12 by Max Wenqiang Xu, Xu, Max Wenqiang · 3 citations
Computer Science · #Classical Analysis and ODEs (math.CA) #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2303.06774

openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate when the better than square-root cancellation phenomenon exists for ∑_{n≤ N}a(n)f(n), where a(n)∈ ℂ and f(n) is a random multiplicative function. We focus on the case where a(n) is the indicator function of R rough numbers. We prove that log log R \asymp (log log x)^(1)/(2) is the threshold for the better than square-root cancellation phenomenon to disappear.

Cited by

• Central limit theorems for random multiplicative functions over function fields
• Helson's conjecture for smooth numbers
• Random Multiplicative Functions with Periodic Weights

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