{
  "id": "1606.04049",
  "version": "v1",
  "published": "2016-06-13T18:05:56.000Z",
  "updated": "2016-06-13T18:05:56.000Z",
  "title": "The Distribution of Integers in a Totally Real Cubic Field",
  "authors": [
    "Tianyi Mao"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of given trace in a general totally real number field of any degree. When the field is cubic, we show that the asymptotic behavior of a weighted Diophantine sum is related to the structure of the unit group. The main term can be expressed in terms of Gr\\\"ossencharacter $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-13T18:05:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally real cubic field",
      "distribution",
      "general totally real number field",
      "hecke studies",
      "quadratic irrationals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}