{
  "id": "2307.14564",
  "version": "v1",
  "published": "2023-07-27T00:54:59.000Z",
  "updated": "2023-07-27T00:54:59.000Z",
  "title": "An improved error term for $D_4$-quartic fields",
  "authors": [
    "Kevin J. McGown",
    "Amanda Tucker"
  ],
  "comment": "11 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that the number of quartic fields $K$ with discriminant $|\\Delta_K|\\leq X$ whose Galois closure is $D_4$ equals $CX+O(X^{3/5+\\epsilon})$, improving the error term in a well-known result of Cohen, Diaz y Diaz, and Olivier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-27T00:54:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N45",
      "11R45",
      "11R16"
    ],
    "keywords": [
      "quartic fields",
      "error term",
      "well-known result",
      "galois closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}