{
  "id": "1909.01338",
  "version": "v2",
  "published": "2019-09-03T17:59:57.000Z",
  "updated": "2022-01-06T01:51:08.000Z",
  "title": "A zero density estimate for Dedekind zeta functions",
  "authors": [
    "Jesse Thorner",
    "Asif Zaman"
  ],
  "comment": "Considerably streamlined, small refinements to Theorems 1.1 and 1.2. 14 pages",
  "doi": "10.1093/imrn/rnac015",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a nontrivial finite group $G$, we prove the first zero density estimate for families of Dedekind zeta functions associated to Galois extensions $K/\\mathbb{Q}$ with $\\mathrm{Gal}(K/\\mathbb{Q})\\cong G$ that does not rely on unproven progress towards the strong form of Artin's conjecture. We use this to remove the hypothesis of the strong Artin conjecture from the work of Pierce, Turnage-Butterbaugh, and Wood on the average error in the Chebotarev density theorem and $\\ell$-torsion in ideal class groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-06T01:51:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dedekind zeta functions",
      "first zero density estimate",
      "nontrivial finite group",
      "chebotarev density theorem",
      "ideal class groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}