{
  "id": "1906.09718",
  "version": "v1",
  "published": "2019-06-24T04:27:21.000Z",
  "updated": "2019-06-24T04:27:21.000Z",
  "title": "Lower bound for class number and a proof of Chowla and Yokoi's conjecture",
  "authors": [
    "Mohit Mishra"
  ],
  "comment": "21 pages. Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d$ be a square-free positive integer and $h(d)$ the class number of the real quadratic field $\\mathbb{Q}{(\\sqrt{d})}.$ In this paper we give an explicit lower bound for $h(n^2+r)$, where $r=1,4$, and also establish an equivalent criteria to attain this lower bound in terms of special value of Dedekind zeta function. Our bounds enables us to provide a new proof of a well-known conjecture of Chowla and that of Yokoi. Also applying our results, we obtain some criteria for class group of prime power order to be cyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-24T04:27:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R42",
      "11R11"
    ],
    "keywords": [
      "class number",
      "yokois conjecture",
      "real quadratic field",
      "explicit lower bound",
      "dedekind zeta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}