{
  "id": "0905.4372",
  "version": "v1",
  "published": "2009-05-27T10:37:13.000Z",
  "updated": "2009-05-27T10:37:13.000Z",
  "title": "On mod p representations which are defined over F_p: II",
  "authors": [
    "L. J. P. Kilford",
    "Gabor Wiese"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\\chi}_{l,k} for all primes l, all weights k>1 and all characters \\chi taking values in {+1,-1} splits completely modulo p has density 0, unconditionally for p=2 and under the Cohen-Lenstra heuristics for odd p. The method of proof is based on the construction of suitable dihedral modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-27T10:37:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F25",
      "11R29"
    ],
    "keywords": [
      "representations",
      "hecke polynomials modulo",
      "suitable dihedral modular forms",
      "cohen-lenstra heuristics",
      "characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4372K"
    }
  }
}