{
  "id": "1912.12754",
  "version": "v1",
  "published": "2019-12-29T23:09:19.000Z",
  "updated": "2019-12-29T23:09:19.000Z",
  "title": "On the occurrence of Hecke eigenvalues in sectors",
  "authors": [
    "Nahid Walji"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a non-self-dual unitary cuspidal automorphic representation of non-solvable polyhedral type for GL(2) over a number field. We show that $\\pi$ has a positive upper Dirichlet density of Hecke eigenvalues in any sector whose angle is at least 2.64 radians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-29T23:09:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F41",
      "11F66"
    ],
    "keywords": [
      "hecke eigenvalues",
      "non-self-dual unitary cuspidal automorphic representation",
      "occurrence",
      "positive upper dirichlet density",
      "non-solvable polyhedral type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}