{
  "id": "1703.02840",
  "version": "v1",
  "published": "2017-03-08T14:07:51.000Z",
  "updated": "2017-03-08T14:07:51.000Z",
  "title": "On the irreducibility and Galois group of Hecke polynomials",
  "authors": [
    "Paloma Bengoechea"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let T_{n,2k}(X) be the characteristic polynomial of the n-th Hecke operator acting on the space of cusp forms of weight 2k for the full modular group (k is any even positive integer >5). We show that if there exists n>1 such that T_{n,2k}(X) is irreducible and has the full symmetric group as Galois group, then the same is true of T_{p,2k}(X) for all primes p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-08T14:07:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois group",
      "hecke polynomials",
      "irreducibility",
      "full symmetric group",
      "full modular group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}