{
  "id": "2001.00865",
  "version": "v1",
  "published": "2020-01-03T15:50:48.000Z",
  "updated": "2020-01-03T15:50:48.000Z",
  "title": "The rank of the 2-class group of some fields with large degree",
  "authors": [
    "Mohamed Mahmoud Chems-Eddin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d$ be an odd square-free integer, $k= \\mathbb{Q}(\\sqrt{d}, \\sqrt{-1})$ and $L_{n,d}=\\mathbb{Q}(\\zeta_{2^n},\\sqrt{d})$, with $n\\geq 3$ is an integer. We compute the rank of the $2$-class group of $L_{n,d}$ when all the divisors of $d$ are congruent to $9\\pmod{16}$. Furthermore, we give the rank of the $2$-class group of $ L_{n,d}$ according to the one of $ L_{4,d}$, when the divisors of $d$ are congruent to $7$ or $9\\pmod{16}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-03T15:50:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large degree",
      "class group",
      "odd square-free integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}