{
  "id": "0707.0237",
  "version": "v2",
  "published": "2007-07-02T19:58:05.000Z",
  "updated": "2007-08-14T19:31:12.000Z",
  "title": "The number of imaginary quadratic fields with a given class number",
  "authors": [
    "K. Soundararajan"
  ],
  "comment": "6 pages; Version 2 has some light changes",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the number ${\\Cal F}(h)$ of imaginary quadratic fields with class number $h$. We establish an asymptotic formula for the average value of ${\\Cal F}(h)$. We also establish a modest non-trivial upper bound for ${\\Cal F}(h)$ and give an application to a question of Rosen and Silverman on the odd part of the class number. Finally, we speculate on the asymptotic nature of ${\\Cal F}(h)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-14T19:31:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "class number",
      "modest non-trivial upper bound",
      "asymptotic formula",
      "average value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0237S"
    }
  }
}