Pair correlation of $\hat{I}\pm n^{\hat{I}}¸$ for random $\hat{I}¸$

Andrei Shubin

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