{
  "id": "1911.12838",
  "version": "v1",
  "published": "2019-11-28T19:28:16.000Z",
  "updated": "2019-11-28T19:28:16.000Z",
  "title": "Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on $\\mathbb{Q}$-rank one arithmetic quotients",
  "authors": [
    "Iver Walkoe"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdi{\\`e}re's use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup methods. We use this to prove meromorphic continuation of Eisenstein series in several $\\mathbb{Q}$-rank one cases, again following Colin de Verdi{\\`e}re, as opposed to the semigroup-oriented viewpoint of Lax-Phillips and W. Mueller.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-28T19:28:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55"
    ],
    "keywords": [
      "meromorphic continuation",
      "eisenstein series",
      "arithmetic quotients",
      "spectral decomposition",
      "pseudo-cuspforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}