{
  "id": "1312.2732",
  "version": "v2",
  "published": "2013-12-10T09:54:14.000Z",
  "updated": "2014-10-26T14:20:25.000Z",
  "title": "Asymptotic behaviors of means of central values of automorphic $L$-functions for GL(2)",
  "authors": [
    "Shingo Sugiyama"
  ],
  "comment": "33 pages. Misprints are modified",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathbb{A}$ be the adele ring of a totally real algebraic number field $F$. We push forward an explicit computation of a relative trace formula for periods of automorphic forms along a split torus in $GL(2)$ from a square free level case done by Masao Tsuzuki, to an arbitrary level case. By using a relative trace formula, we study central values of automorphic $L$-functions for cuspidal automorphic representations of $GL(2, \\mathbb{A})$ corresponding to Maass forms with arbitrary level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-10T09:54:14.000Z",
      "comment": "33 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-26T14:20:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F70"
    ],
    "keywords": [
      "asymptotic behaviors",
      "automorphic",
      "relative trace formula",
      "totally real algebraic number field",
      "square free level case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2732S"
    }
  }
}