AI & Computingarticle2026-09-17

Almost sure upper bound for random multiplicative functions

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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.

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View paper (DOI)Open access versionOpenAlexActa ArithmeticaPublished 2026-09-17

Authors: Rachid Caich

Institutions: Université Paris Cité, Sorbonne Université, Centre National de la Recherche Scientifique, Institut de Mathématiques de Jussieu-Paris Rive Gauche