{
  "id": "1710.02789",
  "version": "v1",
  "published": "2017-10-08T06:26:13.000Z",
  "updated": "2017-10-08T06:26:13.000Z",
  "title": "An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms",
  "authors": [
    "Shingo Sugiyama",
    "Masao Tsuzuki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give an exact formula of the average of adjoint $L$-functions of holomorphic Hilbert cusp forms with a fixed weight and a square-free level, which is a generalization of Zagier's formula known for the case of elliptic cusp forms on ${\\rm SL}_2(\\mathbb{Z})$. As an application, we prove that the Satake parameters of Hilbert cusp forms with a fixed weight and with growing square-free levels are equidistributed in an ensemble constructed by values of the adjoint $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-08T06:26:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F72",
      "11F67"
    ],
    "keywords": [
      "hilbert modular forms",
      "explicit trace formula",
      "jacquet-zagier type",
      "holomorphic hilbert cusp forms",
      "square-free level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}