{
  "id": "1906.06103",
  "version": "v1",
  "published": "2019-06-14T10:02:42.000Z",
  "updated": "2019-06-14T10:02:42.000Z",
  "title": "Simple Fourier trace formulas of Cubic Level and Applications",
  "authors": [
    "Qinghua Pi",
    "Yingnan Wang",
    "Lei Zhang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "With the method of the relative trace formula and the classification of simple supercuspidal representations, we establish a simple Petersson trace formula and a simple Kuznetsov trace formula for automorphic forms on $GL(2)$ of cubic level. As applications, we obtain a non-vanishing result for central $L$-values of holomorphic newforms and some Weyl's laws for Maass newforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T10:02:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F72",
      "11F67"
    ],
    "keywords": [
      "simple fourier trace formulas",
      "cubic level",
      "applications",
      "simple petersson trace formula",
      "simple kuznetsov trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}