{
  "id": "2207.10380",
  "version": "v1",
  "published": "2022-07-21T09:24:16.000Z",
  "updated": "2022-07-21T09:24:16.000Z",
  "title": "Lower bound for the $2$-adic valuations of central $L$-values of elliptic curves with complex multiplication",
  "authors": [
    "Keiichiro Nomoto"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E_{4D}$ be the elliptic curve $y^2=x^3-4Dx$ defined over $K=\\mathbb{Q}(i)$ for $D\\in K$ which is coprime to $2$. In this paper, we give a sharp lower bound for the $2$-adic valuation of the algebraic part of the central value of Hecke $L$-function associated with $E_{4D}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-21T09:24:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G15",
      "11G40"
    ],
    "keywords": [
      "elliptic curve",
      "adic valuation",
      "complex multiplication",
      "sharp lower bound",
      "algebraic part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}