{
  "id": "1601.05180",
  "version": "v1",
  "published": "2016-01-20T06:28:35.000Z",
  "updated": "2016-01-20T06:28:35.000Z",
  "title": "On the divisibility of the class numbers and discriminants of imaginary quadratic fields",
  "authors": [
    "Meng Fai Lim"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $n$ be a squarefree positive odd integer. We will show that there exist infinitely many imaginary quadratic number fields with discriminant divisible by $n$ and-at the same time-having an element of order $n$ in the class group. We will also prove certain results on the divisibility of $r(N)$, where $r(N)$ is the representation numbers of $N$ as sums of three squares. Namely, we will show that for a given squarefree positive odd integer $n$ there exist infinitely many $N$ such that $n$ divides both $N$ and $r(N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-20T06:28:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R29",
      "11R70"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "class numbers",
      "squarefree positive odd integer",
      "discriminant",
      "divisibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160105180L"
    }
  }
}