{
  "id": "2101.12400",
  "version": "v1",
  "published": "2021-01-29T04:30:34.000Z",
  "updated": "2021-01-29T04:30:34.000Z",
  "title": "Averages and nonvanishing of central values of triple product $L$-functions",
  "authors": [
    "Bin Guan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f,g,h$ be three normalized cusp newforms of weight $2k$ on $\\Gamma_0(N)$ which are eigenforms of Hecke operators. We use Ichino's period formula combined with a relative trace formula to show exact averages of $L(3k-1,f\\times g\\times h)$. We also present some applications of the average formulas to the nonvanishing problem, giving a lower bound on the number of nonvanishing central $L$-values when one of the forms is fixed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-29T04:30:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F72"
    ],
    "keywords": [
      "central values",
      "triple product",
      "nonvanishing",
      "ichinos period formula",
      "hecke operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}