{
  "id": "1411.2058",
  "version": "v1",
  "published": "2014-11-07T23:01:26.000Z",
  "updated": "2014-11-07T23:01:26.000Z",
  "title": "On the Occurrence of Hecke Eigenvalues and a Lacunarity Question of Serre",
  "authors": [
    "Nahid Walji"
  ],
  "comment": "13 pages. To appear in Mathematical Research Letters",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let \\pi be a unitary cuspidal automorphic representation for GL(n) over a number field. We establish upper bounds on the number of Hecke eigenvalues of \\pi equal to a fixed complex number. For GL(2), we also determine upper bounds on the number of Hecke eigenvalues with absolute value equal to a fixed number \\gamma; in the case \\gamma=0, this answers a question of Serre. These bounds are then improved upon by restricting to non-dihedral representations. Finally, we obtain analogous bounds for a family of cuspidal automorphic representations for GL(3).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T23:01:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke eigenvalues",
      "lacunarity question",
      "unitary cuspidal automorphic representation",
      "occurrence",
      "absolute value equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2058W"
    }
  }
}