{
  "id": "0912.1692",
  "version": "v1",
  "published": "2009-12-09T09:20:26.000Z",
  "updated": "2009-12-09T09:20:26.000Z",
  "title": "Eigenvalues of Hecke operators on Hilbert modular groups",
  "authors": [
    "Roelof W. Bruggeman Roberto J. Miatello"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider cuspidal representations in spaces of automorphic forms for the congruence subgroup $\\Gamma_0(I)$ of Hilbert modular groups for some number field $F$. To each such representation are associated the eigenvalue $\\lambda_j$ of the Casimir operator at each real place $j$ of $F$, and the number $\\ld_{\\mathfrak p}$ parametrizing the eigenvalue of the Hecke operator $T_{\\mathfrak p^2}$ at each finite place $\\mathfrak p$ outside the ideal $I$. We study the joint distribution of the $\\lambda_j$ for all real places $j$, and the $\\ld_{\\mathfrak p}$ for finitely many $\\mathfrak p$ outside $I$, over the cuspidal representations. This distribution is given by the product of the Plancherel measure at each real place and the Sato-Tate measure at each finite place.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-09T09:20:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41",
      "11F60",
      "11F72",
      "22E30"
    ],
    "keywords": [
      "hilbert modular groups",
      "hecke operator",
      "real place",
      "eigenvalue",
      "finite place"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1692M"
    }
  }
}