{
  "id": "2005.12646",
  "version": "v1",
  "published": "2020-05-26T11:58:21.000Z",
  "updated": "2020-05-26T11:58:21.000Z",
  "title": "Small class number fields in the family $\\mathbb{Q}(\\sqrt{9m^2+4m})$",
  "authors": [
    "Nimish Mahapatra",
    "Prem Prakash Pandey",
    "Mahesh Ram"
  ],
  "comment": "20 pages. Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the class number one problem for real quadratic fields $\\mathbb{Q}(\\sqrt{9m^2+ 4m})$, where $m$ is an odd integer. We show that for $m \\equiv 1 \\pmod 3$ there is only one such field with class number one and only one such field with class number two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T11:58:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R29"
    ],
    "keywords": [
      "small class number fields",
      "real quadratic fields",
      "odd integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}