论文信息 - The distribution of spacings between the fractional parts of n2α

The distribution of spacings between the fractional parts of n2α

We study the distribution of normalized spacings between the fractional parts of an^2, n=1,2,.... We conjecture that if a is "badly approximable" by rationals, then the sequence of fractional parts has Poisson spacings, and give a number of results towards this conjecture. We also present an example of a Diophantine number a for which the higher correlation functions of the sequence blow up.

Peter Sarnak | Alexandru Zaharescu | Zeev Rudnick

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