The distribution of spacings between the fractional parts of $n^2 \alpha$
Rudnick, Zeev ; Sarnak, Peter ; Zaharescu, Alexandru
arXiv, 0002139 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-02-17
Classification:  Mathematics - Number Theory,  Mathematical Physics 
@article{0002139,
     author = {Rudnick, Zeev and Sarnak, Peter and Zaharescu, Alexandru},
     title = {The distribution of spacings between the fractional parts of $n^2
  \alpha$},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002139}
}

Rudnick, Zeev; Sarnak, Peter; Zaharescu, Alexandru. The distribution of spacings between the fractional parts of $n^2
  \alpha$. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002139/