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arXiv · 2610.00843

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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Sun-Kai Leung. 2026-09-30. Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets. https://arxiv.org/abs/2610.00843

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