{
  "id": "0810.0425",
  "version": "v3",
  "published": "2008-10-02T14:36:17.000Z",
  "updated": "2008-10-22T06:29:01.000Z",
  "title": "Rankin Triple Products and Quantum Chaos",
  "authors": [
    "Thomas C. Watson"
  ],
  "comment": "58 pages. A reformatted version, with minor revisions, of my Ph.D. thesis (Princeton 2002, adviser: Peter Sarnak). For the original, see 0810.0425v1.",
  "categories": [
    "math.NT",
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We prove explicit Harris-Kudla type formulas for triples of Maass forms, holomorphic forms, and combinations thereof, on the hyperbolic plane modulo congruence groups and co-compact lattices arising from Eichler orders of quaternion algebras. These formulas relate the central value of the corresponding Rankin triple product L-function to a squared trilinear period integral. Assuming subconvexity estimates for these L-values, we prove Quantum Unique Ergodicity on such quotients; the relevant Lindelof hypotheses imply a quantitative form of QUE, with an optimal rate. In connection with the Berry/Hejhal Random Wave conjecture, we prove decay of third moments in the high energy limit, making use of a subconvexity result of Iwaniec/Ivic/Jutila and Kim-Shahidi's result on cuspidality of the symmetric cube.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-22T06:29:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q50",
      "11F27",
      "11M26",
      "37A45"
    ],
    "keywords": [
      "quantum chaos",
      "hyperbolic plane modulo congruence groups",
      "corresponding rankin triple product l-function",
      "explicit harris-kudla type formulas",
      "berry/hejhal random wave conjecture"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0425W"
    }
  }
}