{
  "id": "math/0311335",
  "version": "v1",
  "published": "2003-11-19T20:12:19.000Z",
  "updated": "2003-11-19T20:12:19.000Z",
  "title": "Weyl's law for the cuspidal spectrum of SL(n)",
  "authors": [
    "Werner Mueller"
  ],
  "comment": "56 pages",
  "categories": [
    "math.RT",
    "math.NT",
    "math.SP"
  ],
  "abstract": "Let $\\Gamma$ be a principal congruence subgroup of $SL_n(Z)$ and let $\\sigma$ be an irreducible representation of SO(n). Let $N(T,\\sigma)$ be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for $\\Gamma$ which transform under SO(n) according to $\\sigma$. We prove that the counting function $N(T,\\sigma)$ satisfies Weyl's law as $T\\to\\infty$. Especially this implies that there exist infinitely many cusp forms for the full modular group $SL_n(Z)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-19T20:12:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "58G25"
    ],
    "keywords": [
      "cuspidal spectrum",
      "cusp forms",
      "full modular group",
      "principal congruence subgroup",
      "satisfies weyls law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11335M"
    }
  }
}