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

arXiv eprints
 Pub Date:
 July 2021
 DOI:
 10.48550/arXiv.2107.07092
 arXiv:
 arXiv:2107.07092
 Bibcode:
 2021arXiv210707092R
 Keywords:

 Mathematics  Number Theory
 EPrint:
 Corrected typos, and fixed a bug in Section 2.3 which was pointed out by Shvo Regavim