{
  "id": "1408.5650",
  "version": "v1",
  "published": "2014-08-25T01:25:01.000Z",
  "updated": "2014-08-25T01:25:01.000Z",
  "title": "Generation of class fields by using the Weber function",
  "authors": [
    "Ja Kyung Koo",
    "Dong Hwa Shin",
    "Dong Sung Yoon"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be an imaginary quadratic field and $\\mathcal{O}_K$ be its ring of integers. Let $h_E$ be the Weber function on a certain elliptic curve $E$ with complex multiplication by $\\mathcal{O}_K$. We show that if $N>1$ is an integer prime to $6$, then the value of $h_E$ at some $N$-torsion point of $E$ generates the ray class field modulo $N\\mathcal{O}_K$ over $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-25T01:25:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37",
      "11G15",
      "11G16"
    ],
    "keywords": [
      "weber function",
      "generation",
      "ray class field modulo",
      "imaginary quadratic field",
      "integer prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5650K"
    }
  }
}