{
  "id": "math/0002139",
  "version": "v2",
  "published": "2000-02-17T09:57:40.000Z",
  "updated": "2001-01-04T12:25:04.000Z",
  "title": "The distribution of spacings between the fractional parts of $n^2 α$",
  "authors": [
    "Zeev Rudnick",
    "Peter Sarnak",
    "Alexandru Zaharescu"
  ],
  "comment": "Substantial revisions in the exposition. Accepted for publication in Inventiones mathematicae",
  "doi": "10.1007/s002220100141",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-01-04T12:25:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional parts",
      "distribution",
      "higher correlation functions",
      "conjecture",
      "poisson spacings"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2001,
      "month": "Jul",
      "volume": 145,
      "number": 1,
      "pages": 37
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001InMat.145...37R"
    }
  }
}