{
  "id": "1907.12097",
  "version": "v1",
  "published": "2019-07-28T15:37:10.000Z",
  "updated": "2019-07-28T15:37:10.000Z",
  "title": "On the simultaneous divisibility of class numbers of triples of imaginary quadratic fields",
  "authors": [
    "Jaitra Chattopadhyay",
    "Subramani Muthukrishnan"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k \\geq 1$ be a cube-free integer with $k \\equiv 1 \\pmod {9}$ and $\\gcd(k, 7\\cdot 571)=1$. In this paper, we prove the existence of infinitely many triples of imaginary quadratic fields $\\mathbb{Q}(\\sqrt{d})$, $\\mathbb{Q}(\\sqrt{d+1})$ and $\\mathbb{Q}(\\sqrt{d+k^2})$ with $d \\in \\mathbb{Z}$ such that the class number of each of them is divisible by $3$. This affirmatively answers a weaker version of a conjecture of Iizuka \\cite{iizuka-jnt}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-28T15:37:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "class number",
      "simultaneous divisibility",
      "cube-free integer",
      "weaker version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}