{
  "id": "1601.02526",
  "version": "v1",
  "published": "2016-01-11T17:23:59.000Z",
  "updated": "2016-01-11T17:23:59.000Z",
  "title": "Quantum variance on quaternion algebras, I",
  "authors": [
    "Paul D. Nelson"
  ],
  "comment": "36 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular curve, whose method required a cusp. Our method uses the theta correspondence to reduce the problem to the estimation of metaplectic Rankin--Selberg convolutions. We illustrate it here in the simplest non-trivial non-split case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-11T17:23:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11F37",
      "58J51"
    ],
    "keywords": [
      "quantum variance",
      "simplest non-trivial non-split case",
      "non-split quaternion algebra",
      "metaplectic rankin-selberg convolutions",
      "theta correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102526N"
    }
  }
}