{
  "id": "1406.2902",
  "version": "v1",
  "published": "2014-06-11T13:42:28.000Z",
  "updated": "2014-06-11T13:42:28.000Z",
  "title": "Existence of Hilbert cusp forms with non-vanishing $L$-values",
  "authors": [
    "Shingo Sugiyama",
    "Masao Tsuzuki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we prove existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-11T13:42:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F72"
    ],
    "keywords": [
      "hilbert cusp forms",
      "hecke fields",
      "non-vanishing central values",
      "absolute degrees",
      "relative trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2902S"
    }
  }
}