{
  "id": "math/9907202",
  "version": "v1",
  "published": "1999-07-01T00:00:00.000Z",
  "updated": "1999-07-01T00:00:00.000Z",
  "title": "Analytic continuation of representations and estimates of automorphic forms",
  "authors": [
    "Joseph Bernstein",
    "Andre Reznikov"
  ],
  "comment": "24 pages, published version, abstract added in migration",
  "journal": "Ann. of Math. (2) 150 (1999), no. 1, 329-352",
  "categories": [
    "math.RT"
  ],
  "abstract": "Properties of analytic vectors in representations of SL(2,R) are used to give new bounds for the triple products recently considered by P. Sarnak. A conjecture of Sarnak about such products is proved. The results of this paper generalize results of A. Good and M. Jutila about special cases, but the techniques are entirely different. One consequence of these results is a new estimate of the magnitude of the Fourier coefficients of cusp forms for non-arithmetic sub-groups of SL(2,R).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphic forms",
      "analytic continuation",
      "representations",
      "non-arithmetic sub-groups",
      "analytic vectors"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7202B"
    }
  }
}