On the number of gaps of sequences with Poissonian Pair Correlations

Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1

A sequence $(x_n)$ on the torus is said to have Poissonian pair correlations if $\#\{1\le i\ne j\le N:|x_i-x_j|\le s/N\}=2sN(1+o(1))$ for all reals $s>0$, as $N\to \infty$. It…