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

Details The distribution of spacings between the fractional parts of $n^2 α$ The distribution of spacings between the fractional parts of $n^2 α$

2000-02-17

arxiv.org/abs/math/0002139v2

Mathematics

Number Theory

Substantial revisions in the exposition. Accepted for publication in Inventiones mathematicae

Scientific paper

10.1007/s002220100141

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.

Affiliated with

Also associated with

No associations

Rating

The distribution of spacings between the fractional parts of $n^2 α$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The distribution of spacings between the fractional parts of $n^2 α$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The distribution of spacings between the fractional parts of $n^2 α$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312796