{
  "id": "2011.14348",
  "version": "v1",
  "published": "2020-11-29T11:58:07.000Z",
  "updated": "2020-11-29T11:58:07.000Z",
  "title": "Discriminant and Integral basis of sextic fields defined by x^6+ax+b",
  "authors": [
    "Sumandeep Kaur",
    "Sudesh Kaur Khanduja"
  ],
  "comment": "46 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K=\\mathbb Q(\\theta)$ be an algebraic number field with $\\theta$ a root of an irreducible trinomial $f(x)=x^6+ax+b$ belonging to $\\mathbb{Z}[x]$. In this paper, for each prime number $p$ we compute the highest power of $p$ dividing the discriminant of $K$ in terms of the prime powers dividing $a,~b$ and discriminant of $f(x)$. An explicit $p$-integral basis of $K$ is also given for each prime $p$ and a method is described to obtain an integral basis of $K$ from these $p$-integral bases which is illustrated with examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-29T11:58:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R29"
    ],
    "keywords": [
      "integral basis",
      "sextic fields",
      "discriminant",
      "algebraic number field",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}