{
  "id": "math/0512355",
  "version": "v2",
  "published": "2005-12-15T11:16:19.000Z",
  "updated": "2006-08-28T10:22:51.000Z",
  "title": "A realization of the Hecke algebra on the space of period functions for Gamma_0(n)",
  "authors": [
    "M. Fraczek",
    "D. Mayer",
    "T. Mühlenbruch"
  ],
  "comment": "30 pages; corrected typos and fixed incomplete proofs in section 3",
  "journal": "J. Reine Angew. Math. 603 (2007), 133--163",
  "doi": "10.1515/CRELLE.2007.014",
  "categories": [
    "math.NT"
  ],
  "abstract": "The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-28T10:22:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F25",
      "11F67",
      "37C30",
      "37D20",
      "81Q50"
    ],
    "keywords": [
      "hecke algebra",
      "vector valued period functions",
      "maass cusp forms",
      "aforementioned non standard realization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12355F"
    }
  }
}