{
  "id": "1711.06481",
  "version": "v1",
  "published": "2017-11-17T10:18:15.000Z",
  "updated": "2017-11-17T10:18:15.000Z",
  "title": "On the Non-Vanishing of Poincaré Series on the Metaplectic Group",
  "authors": [
    "Sonja Žunar"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "In this paper, we study the $ K $-finite matrix coefficients of integrable representations of the metaplectic cover of $ \\mathrm{SL}_2(\\mathbb R) $ and give a result on the non-vanishing of their Poincar\\'{e} series. We do this by adapting the techniques developed for $ \\mathrm{SL}_2(\\mathbb R) $ by Mui\\'{c} to the case of the metaplectic group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-17T10:18:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "11F12"
    ],
    "keywords": [
      "metaplectic group",
      "non-vanishing",
      "finite matrix coefficients",
      "metaplectic cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}