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PreprintCC BY 4.0arXiv

Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets

  • Sun-Kai Leung
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Abstract

Adapting the circle method developed by Frantzikinakis--Klurman--Moreira, we establish a sufficient criterion for a set of natural numbers to be multiplicatively recurrent. We apply this criterion to Piatetski--Shapiro sets with small exponents and to regular irrational nil-Bohr sets. We also study the value distribution of unimodular completely multiplicative functions along these sets.

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Cite

BibTeXRIS
BibTeX
@misc{leung2026multiplicative,
  title = {{Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets}},
  author = {Sun-Kai Leung},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00843},
  eprint = {2610.00843},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00843},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets
AU  - Sun-Kai Leung
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00843
UR  - https://arxiv.org/abs/2610.00843
AB  - Adapting the circle method developed by Frantzikinakis--Klurman--Moreira, we establish a sufficient criterion for a set of natural numbers to be multiplicatively recurrent. We apply this criterion to Piatetski--Shapiro sets with small exponents and to regular irrational nil-Bohr sets. We also study the value distribution of unimodular completely multiplicative functions along these sets.
ER  -