Almost sure upper bound for random multiplicative functions

Let ε>0. Let f be a Steinhaus or Rademacher random multiplicative function. We prove that almost surely, as x→+∞, ∑n⩽xf(n)≪x√(log2x)3/4+ε.

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Publication Details

Journal
Acta Arithmetica
Published
2026-09-17
DOI
https://doi.org/10.4064/aa250225-20-2
Citations
3
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00
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article

Almost sure upper bound for random multiplicative functions

Rachid Caich
3 citations
Acta Arithmetica
Analytic Number Theory Research
article

Almost sure upper bound for random multiplicative functions

Rachid Caich
article en
3 citations

Abstract

Let ε>0. Let f be a Steinhaus or Rademacher random multiplicative function. We prove that almost surely, as x→+∞, ∑n⩽xf(n)≪x√(log2x)3/4+ε.

Acta Arithmetica
Centre National de la Recherche Scientifique (FR), Université Paris Cité (FR), Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR), Sorbonne Université (FR)
Openalex Percentile: Top 99%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Almost sure upper bound for random multiplicative functions — Rachid Caich · Acta Arithmetica (2026) | TGRS Research Map | TGRS