{
  "id": "1308.0754",
  "version": "v3",
  "published": "2013-08-03T22:22:25.000Z",
  "updated": "2014-05-07T17:40:07.000Z",
  "title": "On the Pair Correlation Density for Hyperbolic Angles",
  "authors": [
    "Dubi Kelmer",
    "Alex Kontorovich"
  ],
  "comment": "35 pages, 5 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Gamma< \\mathrm{PSL}_2(\\mathbb{R})$ be a lattice and $\\omega\\in \\mathbb{H}$ a point in the upper half plane. We prove the existence and give an explicit formula for the pair correlation density function for the set of angles between geodesic rays of the lattice $\\Gamma \\omega$ intersected with increasingly large balls centered at $\\omega$, thus proving a conjecture of Boca-Popa-Zaharescu.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-07T17:40:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic angles",
      "pair correlation density function",
      "upper half plane",
      "explicit formula",
      "geodesic rays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0754K"
    }
  }
}