{
  "id": "1605.01145",
  "version": "v1",
  "published": "2016-05-04T04:59:38.000Z",
  "updated": "2016-05-04T04:59:38.000Z",
  "title": "The Beilinson Conjecture for CM Elliptic Curves via Hypergeometric Functions",
  "authors": [
    "Ryojun Ito"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider certain CM elliptic curves which are related to Fermat curves, and express the values of $L$-functions at $s=2$ in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjecture originally due to Bloch.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-04T04:59:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11S40",
      "19F27",
      "33C20"
    ],
    "keywords": [
      "cm elliptic curves",
      "beilinson conjecture",
      "otsubos regulator formulas",
      "fermat curves",
      "special values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}