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

Zeév Rudnick, Niclas Technau

Published 2021-07-15Version 1

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