{
  "id": "1501.01003",
  "version": "v1",
  "published": "2015-01-05T21:05:07.000Z",
  "updated": "2015-01-05T21:05:07.000Z",
  "title": "Extreme values of class numbers of real quadratic fields",
  "authors": [
    "Youness Lamzouri"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We improve a result of H. L. Montgomery and J. P. Weinberger by establishing the existence of infinitely many fundamental discriminants $d>0$ for which the class number of the real quadratic field $\\mathbb{Q}(\\sqrt{d})$ exeeds $(2e^{\\gamma}+o(1)) \\sqrt{d}(\\log\\log d)/\\log d$. We believe this bound to be best possible. We also obtain a lower bound (unconditionally) and an upper bound (assuming GRH), of nearly the same order of magnitude, for the number of real quadratic fields with discriminant $d\\leq x$ which have such an extreme class number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-05T21:05:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real quadratic field",
      "extreme values",
      "extreme class number",
      "fundamental discriminants",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150101003L"
    }
  }
}