{
  "id": "1706.09987",
  "version": "v1",
  "published": "2017-06-30T00:45:02.000Z",
  "updated": "2017-06-30T00:45:02.000Z",
  "title": "The shape of quartic fields",
  "authors": [
    "Robert Hough"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the joint cuspidal equidistribution of the shape of quartic fields paired with the shape of its cubic resolvent, when the fields are ordered by discriminant. Our estimate saves a small power in the corresponding Weyl sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-30T00:45:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quartic fields",
      "joint cuspidal equidistribution",
      "cubic resolvent",
      "estimate saves",
      "small power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}