{
  "id": "1203.6667",
  "version": "v1",
  "published": "2012-03-29T20:59:08.000Z",
  "updated": "2012-03-29T20:59:08.000Z",
  "title": "On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions",
  "authors": [
    "Dorian Goldfeld",
    "Alex Kontorovich"
  ],
  "comment": "43 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We present an explicit approach to the GL(3) Kuznetsov formula. As an application, for a restricted class of test functions, we obtain the low-lying zero densities for the following three families: cuspidal GL(3) Maass forms phi, the symmetric square family sym^2 phi on GL(6), and the adjoint family Ad phi on GL(8). Hence we can identify their symmetry types; they are: unitary, unitary, and symplectic, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-29T20:59:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66"
    ],
    "keywords": [
      "symmetry types",
      "kuznetsov formula",
      "application",
      "maass forms phi",
      "adjoint family ad phi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6667G"
    }
  }
}