Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets
Sun-Kai Leung
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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad