%0 Journal Article
%T Pair Correlation for Fractional Parts of $¦Án^2$
%A D. R. Heath-Brown
%J Mathematics
%D 2009
%I arXiv
%R 10.1017/S0305004109990466
%X We construct real numbers $\alpha$ for which the pair correlation function \[N^{-1}#\{m<n\le N:||\alpha m^2-\alpha n^2||\le XN^{-1}\}\] tends to $X$ as $N$ grows. Moreover we show for any "Diophantine" $\alpha$ that the pair correlation function is $X+O(X^{7/8})+O((\log N)^{-1}$ for $1\le X\le\log N$.
%U http://arxiv.org/abs/0904.0714v1