A self-normalized law of the iterated logarithm for Rademacher random multiplicative functions

Let $f$ be a Rademacher random multiplicative function supported on the squarefree integers, and let $M(x)=\sum_{n\le x}f(n)$. We prove a two-sided law of the iterated logarithm normalized by the full predictable quadratic variation \[ Q(x)=\sum_{p\le x}\bigg(\sum_{\substack{m\le x/p\\ P(m)

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40605
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

A self-normalized law of the iterated logarithm for Rademacher random multiplicative functions

Dariusz Buraczewski, Alexander Iksanov
arXiv (Cornell University)
Analytic Number Theory Research
preprint

A self-normalized law of the iterated logarithm for Rademacher random multiplicative functions

Dariusz Buraczewski, Alexander Iksanov
preprint en

Abstract

Let $f$ be a Rademacher random multiplicative function supported on the squarefree integers, and let $M(x)=\sum_{n\le x}f(n)$. We prove a two-sided law of the iterated logarithm normalized by the full predictable quadratic variation \[ Q(x)=\sum_{p\le x}\bigg(\sum_{\substack{m\le x/p\\ P(m)

arXiv (Cornell University)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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A self-normalized law of the iterated logarithm for Rademacher random multiplicative functions — Dariusz Buraczewski, Alexander Iksanov · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS