{
  "id": "1309.7849",
  "version": "v3",
  "published": "2013-09-30T14:10:47.000Z",
  "updated": "2014-09-11T08:57:39.000Z",
  "title": "Algebraic $S$-integers of fixed degree and bounded height",
  "authors": [
    "Fabrizio Barroero"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1305.0482, accepted for publication on Acta Arithmetica",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be a number field and $S$ a finite set of places of $k$ containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of $S$-integers of $k$. Moreover, we give an asymptotic formula for the number of $\\bar{S}$-integers of bounded height and fixed degree over $k$, where $\\bar{S}$ is the set of places of $\\bar{k}$ lying above the ones in $S$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-28T15:26:36.000Z",
      "comment": "arXiv admin note: text overlap with arXiv:1305.0482",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-11T08:57:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11R04"
    ],
    "keywords": [
      "bounded height",
      "fixed degree",
      "number field",
      "asymptotic formula",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7849B"
    }
  }
}