{
  "id": "1801.00392",
  "version": "v1",
  "published": "2018-01-01T04:29:11.000Z",
  "updated": "2018-01-01T04:29:11.000Z",
  "title": "Exponents of class groups of certain imaginary quadratic fields",
  "authors": [
    "Azizul Hoque",
    "Kalyan Chakraborty"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\\mathbb{Q}(\\sqrt{x^2-2y^n})$ whose ideal class group has an element of order $n$. This family gives a counter example to a conjecture by H. Wada \\cite{WA70} on the structure of ideal class groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-01T04:29:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R11"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "ideal class group",
      "odd integer",
      "counter example",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}