{
  "id": "1302.3112",
  "version": "v1",
  "published": "2013-02-13T14:23:19.000Z",
  "updated": "2013-02-13T14:23:19.000Z",
  "title": "Spectral large sieve inequalities for Hecke congruence subgroups of SL(2,Z[i])",
  "authors": [
    "Nigel Watt"
  ],
  "comment": "137 pages, 0 figures",
  "journal": "J. Number Theory 140 (2014), 349-424",
  "doi": "10.1016/j.jnt.2014.01.018",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove, in respect of an arbitrary Hecke congruence subgroup \\Gamma =\\Gamma_0(q_0) of the group SL(2,Z[i]), some new upper bounds (or `spectral large sieve inequalities') for sums involving Fourier coefficients of \\Gamma -automorphic cusp forms on SL(2,C). The Fourier coefficients in question may arise from the Fourier expansion at any given cusp c of \\Gamma : our results are not limited to the case in which c is the cusp at infinity. For this reason, our proof is reliant upon an extension, to arbitrary cusps, of the spectral-Kloosterman sum formula for \\Gamma\\SL(2,C) obtained by Hristina Lokvenec-Guleska in her doctoral thesis (generalising the sum formulae of Roelof Bruggeman and Yoichi Motohashi for PSL(2,Z[i])\\PSL(2,C) in several respects, though not as regards the choice of cusps). A proof of the required extension of the sum formula is given in an appendix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-13T14:23:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F37",
      "11F70",
      "11F72",
      "11L05",
      "11L07",
      "11M41",
      "11N35",
      "11R42",
      "22E30",
      "33C10",
      "44A15"
    ],
    "keywords": [
      "spectral large sieve inequalities",
      "fourier coefficients",
      "arbitrary hecke congruence subgroup",
      "spectral-kloosterman sum formula",
      "automorphic cusp forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 137,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3112W"
    }
  }
}