{
  "id": "1608.06705",
  "version": "v1",
  "published": "2016-08-24T04:13:13.000Z",
  "updated": "2016-08-24T04:13:13.000Z",
  "title": "On Hasse-Ramachandra's problem",
  "authors": [
    "Ja Kyung Koo",
    "Dong Hwa Shin",
    "Dong Sung Yoon"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be an imaginary quadratic field, and let $N$ be an integer greater than $1$. We show that a special value of the Weber function alone generates the ray class field modulo $N$ over the base field $K$, except for the eight cases $N=2,\\,3,\\,4,\\,6,\\,12,\\,18,\\,24,\\,36$. This would be a partial answer to the question raised by Hasse and Ramachandra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-24T04:13:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37",
      "11G15",
      "11G16"
    ],
    "keywords": [
      "hasse-ramachandras problem",
      "ray class field modulo",
      "imaginary quadratic field",
      "weber function",
      "integer greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}