Pair correlation of $\alpha n^{\theta }$ for random $\theta$

Andrei Shubin

For fixed $\alpha >0$, we show that the sequence $\{\alpha n^{\theta }\}$ has Poissonian pair correlation for Lebesgue-almost all $\theta \in (0,\frac{3}{5})\cup (3,\infty )$. This improves a result of Techna…