{
  "id": "2412.02416",
  "version": "v1",
  "published": "2024-12-03T12:29:40.000Z",
  "updated": "2024-12-03T12:29:40.000Z",
  "title": "A zero-density estimate for $L$-functions associated with $\\rm GL(3)$ Hecke--Maass cusp forms",
  "authors": [
    "Qingfeng Sun",
    "Hui Wang"
  ],
  "comment": "33 pages. Comments welcome! arXiv admin note: text overlap with arXiv:1704.00314 by other authors",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we establish an asymptotic formula for the twisted second moment of $L$-functions associated with Hecke--Maass cusp forms for $\\rm SL(3,\\mathbb{Z})$, and further deduce a weighted zero-density estimate for these $L$-functions in the spectral aspect which may have important applications in other problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-03T12:29:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F12",
      "11F66",
      "11F67",
      "11F72"
    ],
    "keywords": [
      "hecke-maass cusp forms",
      "asymptotic formula",
      "twisted second moment",
      "weighted zero-density estimate",
      "spectral aspect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}