{
  "id": "1007.0593",
  "version": "v1",
  "published": "2010-07-04T22:18:52.000Z",
  "updated": "2010-07-04T22:18:52.000Z",
  "title": "Diophantine approximation and automorphic spectrum",
  "authors": [
    "Anish Ghosh",
    "Alexander Gorodnik",
    "Amos Nevo"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-04T22:18:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine approximation",
      "automorphic spectrum",
      "paper establishes qunatitative estimates",
      "semisimple algebraic groups",
      "automorphic representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0593G"
    }
  }
}