{
  "id": "1810.00762",
  "version": "v1",
  "published": "2018-10-01T15:35:16.000Z",
  "updated": "2018-10-01T15:35:16.000Z",
  "title": "On fundamental Fourier coefficients of Siegel modular forms",
  "authors": [
    "Siegfried Bocherer",
    "Soumya Das"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that if $F$ is a non-zero (possibly non-cuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many non-zero Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting of vector-valued modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T15:35:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F46",
      "11F50"
    ],
    "keywords": [
      "fundamental fourier coefficients",
      "vector-valued siegel modular form",
      "non-zero fourier coefficients",
      "half-integral matrices",
      "induction argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}