The distribution of spacings between the fractional parts of n 2 α

Abstract

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.

Locations

• Inventiones mathematicae - View
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• arXiv (Cornell University) - View - PDF
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• Inventiones mathematicae - View
• arXiv (Cornell University) - View - PDF
• arXiv (Cornell University) - View - PDF
• DataCite API - View