Pair Correlation for Fractional Parts of $\alpha n^2$
Number Theory
2015-05-13 v1
Abstract
We construct real numbers for which the pair correlation function N^{-1}#\{m<n\le N:||\alpha m^2-\alpha n^2||\le XN^{-1}\} tends to as grows. Moreover we show for any "Diophantine" that the pair correlation function is for .
Keywords
Cite
@article{arxiv.0904.0714,
title = {Pair Correlation for Fractional Parts of $\alpha n^2$},
author = {D. R. Heath-Brown},
journal= {arXiv preprint arXiv:0904.0714},
year = {2015}
}