{
  "id": "2408.13682",
  "version": "v1",
  "published": "2024-08-24T22:29:17.000Z",
  "updated": "2024-08-24T22:29:17.000Z",
  "title": "Density theorems for $\\text{GL}_n$ via Rankin-Selberg $L$-functions",
  "authors": [
    "Jared Duker Lichtman",
    "Alexandru Pascadi"
  ],
  "comment": "24 pages; comments welcome!",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We obtain density theorems for cuspidal automorphic representations of $\\text{GL}_n$ over $\\mathbb{Q}$ which fail the generalized Ramanujan conjecture at some place. We depart from previous approaches based on Kuznetsov-type trace formulae, and instead rely on $L$-function techniques. This improves recent results of Blomer near the threshold of the pointwise bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-24T22:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F66",
      "11F30",
      "11R42"
    ],
    "keywords": [
      "density theorems",
      "rankin-selberg",
      "cuspidal automorphic representations",
      "kuznetsov-type trace formulae",
      "function techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}