{
  "id": "1707.01314",
  "version": "v1",
  "published": "2017-07-05T10:55:08.000Z",
  "updated": "2017-07-05T10:55:08.000Z",
  "title": "Congruences between Hilbert modular forms of weight $2$, and special values of their $L$-functions",
  "authors": [
    "Yuichi Hirano"
  ],
  "comment": "43 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The purpose of this paper is to show how a congruence between (the Fourier coefficients of) a Hilbert cusp form and a Hilbert Eisenstein series of parallel weight $2$ gives rise to congruences between algebraic parts of critical values of their $L$-functions. This is a generalization of a result of V. Vatsal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-05T10:55:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F30",
      "11F41",
      "11F67"
    ],
    "keywords": [
      "hilbert modular forms",
      "special values",
      "congruence",
      "hilbert cusp form",
      "hilbert eisenstein series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}