{
  "id": "1302.6094",
  "version": "v1",
  "published": "2013-02-25T14:08:51.000Z",
  "updated": "2013-02-25T14:08:51.000Z",
  "title": "On the Number of Eisenstein Polynomials of Bounded Height",
  "authors": [
    "Randell Heyman",
    "Igor E. Shparlinski"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\\to \\infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-25T14:08:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded height",
      "asymptotic formula",
      "arbitrary eisenstein polynomials",
      "monic eisenstein polynomials",
      "precise version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6094H"
    }
  }
}