{
  "id": "1906.07717",
  "version": "v1",
  "published": "2019-06-18T17:59:59.000Z",
  "updated": "2019-06-18T17:59:59.000Z",
  "title": "The GL(n) large sieve",
  "authors": [
    "Jesse Thorner",
    "Asif Zaman"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\\pi$ of $\\mathrm{GL}_n$ over a number field with unitary central character. We prove an unconditional large sieve inequality for the Hecke eigenvalues of $\\pi\\in\\mathfrak{F}_n$. This leads to the first unconditional zero density estimate for the family of $L$-functions $L(s,\\pi)$ associated to $\\pi\\in\\mathfrak{F}_n$, which we make log-free. As an application, we prove a subconvexity bound on $L(1/2,\\pi)$ for almost all $\\pi\\in\\mathfrak{F}_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-18T17:59:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first unconditional zero density estimate",
      "unconditional large sieve inequality",
      "unitary central character",
      "cuspidal automorphic representations",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}