$2$-large sets are sets of Bohr recurrence

Ryan Alweiss

Let ${\alpha }_1,\cdots ,{\alpha }_d$ be real numbers, and let $S$ be the set of integers $s$ so that $||{\alpha }_{i}s|{|}_{\mathbb{R}/\mathbb{Z}}>\delta$ for some $i$ and some fixed $\delta >0$. We prove $S$ is not…