{
  "id": "2409.08417",
  "version": "v1",
  "published": "2024-09-12T22:29:53.000Z",
  "updated": "2024-09-12T22:29:53.000Z",
  "title": "Lower order terms in the shape of cubic fields",
  "authors": [
    "Robert Hough",
    "Eun Hye Lee"
  ],
  "comment": "Preliminary version. arXiv admin note: substantial text overlap with arXiv:2007.03170",
  "categories": [
    "math.NT"
  ],
  "abstract": "We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T22:29:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower order terms",
      "cubic fields",
      "lower order main term",
      "lattice shape",
      "eisenstein series spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}