{
  "id": "1409.3764",
  "version": "v1",
  "published": "2014-09-12T15:16:31.000Z",
  "updated": "2014-09-12T15:16:31.000Z",
  "title": "Directions in hyperbolic lattices",
  "authors": [
    "Jens Marklof",
    "Ilya Vinogradov"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "It is well known that the orbit of a lattice in hyperbolic $n$-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and express the limit distributions in terms of random hyperbolic lattices. This provides in particular a new perspective on recent results by Boca, Popa, and Zaharescu on 2-point correlations for the modular group, and by Kelmer and Kontorovich for general lattices in dimension $n=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-12T15:16:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directions",
      "random hyperbolic lattices",
      "modular group",
      "general lattices",
      "unit sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.3764M"
    }
  }
}