Pair Correlation for Fractional Parts of $αn^2$

Details Pair Correlation for Fractional Parts of $αn^2$ Pair Correlation for Fractional Parts of $αn^2$

2009-04-04

arxiv.org/abs/0904.0714v1

Mathematics

Number Theory

Scientific paper

We construct real numbers $\alpha$ for which the pair correlation function
\[N^{-1}#\{m$N$ grows. Moreover we show for any "Diophantine" $\alpha$ that the pair
correlation function is $X+O(X^{7/8})+O((\log N)^{-1}$ for $1\le X\le\log N$.

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