The metric theory of the pair correlation function for small non-integer powers

Abstract

For $0<\theta <1$, we show that for almost all $\alpha$, the pair correlation function of the sequence of fractional parts of $\{\alpha n^{\theta }:n\ge 1\}$ is Poissonian.

Corrected typos, and fixed a bug in Section 2.3 which was pointed out by Shvo Regavim