{
  "id": "1902.06429",
  "version": "v1",
  "published": "2019-02-18T07:30:58.000Z",
  "updated": "2019-02-18T07:30:58.000Z",
  "title": "On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\\rm GSp}_4$",
  "authors": [
    "Shih-Yu Chen",
    "Atsushi Ichino"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on ${\\rm GSp}_4$ whose archimedean components belong to either discrete series representations or spherical principal series representations. Our formula expresses the Petersson norms in terms of special values of adjoint $L$-functions and some elementary constants depending only on local representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-18T07:30:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F41",
      "11F27"
    ],
    "keywords": [
      "generic cusp forms",
      "petersson norms",
      "special values",
      "normalized generic cuspidal newforms",
      "archimedean components belong"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}