{
  "id": "2107.07092",
  "version": "v1",
  "published": "2021-07-15T03:05:30.000Z",
  "updated": "2021-07-15T03:05:30.000Z",
  "title": "The metric theory of the pair correlation function for small non-integer powers",
  "authors": [
    "Zeév Rudnick",
    "Niclas Technau"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For $0<\\theta<1$, we show that for almost all $\\alpha$, the pair correlation function of the sequence of fractional parts of $\\{\\alpha n^\\theta:n\\geq 1 \\}$ is Poissonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-15T03:05:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pair correlation function",
      "small non-integer powers",
      "metric theory",
      "fractional parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}