{
  "id": "2204.08868",
  "version": "v1",
  "published": "2022-04-19T13:10:04.000Z",
  "updated": "2022-04-19T13:10:04.000Z",
  "title": "The density conjecture for principal congruence subgroups",
  "authors": [
    "Edgar Assing",
    "Valentin Blomer"
  ],
  "comment": "41 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We prove Sarnak's density conjecture for the principal congruence subgroup of SL_n(Z) of squarefree level and discuss various arithmetic applications. The ingredients include new bounds for local Whittaker functions and Kloosterman sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-19T13:10:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal congruence subgroup",
      "sarnaks density conjecture",
      "local whittaker functions",
      "squarefree level",
      "arithmetic applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}