{
  "id": "1512.07134",
  "version": "v1",
  "published": "2015-12-22T15:54:39.000Z",
  "updated": "2015-12-22T15:54:39.000Z",
  "title": "On the average of the number of imaginary quadratic fields with a given class number",
  "authors": [
    "Youness Lamzouri"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathcal{F}(h)$ be the number of imaginary quadratic fields with class number $h$. In this note, we improve the error term in Soundararajan's asymptotic formula for the average of $\\mathcal{F}(h)$. Our argument leads to a similar refinement of the asymptotic for the average of $\\mathcal{F}(h)$ over odd $h$, which was recently obtained by Holmin, Jones, Kurlberg, McLeman and Petersen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-22T15:54:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "class number",
      "soundararajans asymptotic formula",
      "error term",
      "similar refinement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151207134L"
    }
  }
}