Bohr recurrence and density of non-lacunary semigroups of $\mathbb{N}$
Bohr recurrence and density of non-lacunary semigroups of $\mathbb{N}$
A subset $R$ of integers is a set of Bohr recurrence if every rotation on $\mathbb{T}^d$ returns arbitrarily close to zero under some non-zero multiple of $R$. We show that the set $\{k!\, 2^m3^n\colon k,m,n\in \mathbb{N}\}$ is a set of Bohr recurrence. This is a particular case of a more …