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Peer-reviewedCC BYActa Arithmetica

Almost sure upper bound for random multiplicative functions

  • Rachid Caich1
  1. 1Institut de Mathématiques de Jussieu – Paris Rive Gauche Université Paris Cité Sorbonne Université CNRS 75013 Paris, France
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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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Cite

BibTeXRIS
BibTeX
@article{caich2026almost,
  title = {{Almost sure upper bound for random multiplicative functions}},
  author = {Rachid Caich},
  journal = {Acta Arithmetica},
  year = {2026},
  month = sep,
  doi = {10.4064/aa250225-20-2},
  url = {https://doi.org/10.4064/aa250225-20-2},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Almost sure upper bound for random multiplicative functions
AU  - Rachid Caich
PY  - 2026
DA  - 2026/09/17
JO  - Acta Arithmetica
DO  - 10.4064/aa250225-20-2
UR  - https://doi.org/10.4064/aa250225-20-2
AB  - 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.
SN  - 0065-1036
SN  - 1730-6264
ER  -