{
  "id": "1502.04971",
  "version": "v1",
  "published": "2015-02-17T17:37:55.000Z",
  "updated": "2015-02-17T17:37:55.000Z",
  "title": "The class number formula for imaginary quadratic fields",
  "authors": [
    "Joseph Lewittes"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain information about the distribution of the values of $\\chi(x)$, where $\\chi$ is the quadratic character associated to $D$. This leads to simplified formulas for the class number in certain cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-17T17:37:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "class number formula",
      "integer prime",
      "quadratic character",
      "expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}