{
  "id": "1012.3036",
  "version": "v3",
  "published": "2010-12-14T14:15:31.000Z",
  "updated": "2011-09-30T00:26:15.000Z",
  "title": "From $L$-series of elliptic curves to Mahler measures",
  "authors": [
    "Mathew Rogers",
    "Wadim Zudilin"
  ],
  "comment": "33 pages",
  "journal": "Compositio Mathematica 148 (2012), no. 2, 385-414",
  "doi": "10.1112/S0010437X11007342",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We prove the conjectural relations between Mahler measures and $L$-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for $L$-values of CM elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family $(1+X)(1+Y)(X+Y)-\\alpha XY$, $\\alpha\\in\\mathbb R$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-30T00:26:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R06",
      "33C20",
      "11F03",
      "14H52",
      "19F27",
      "33C75",
      "33E05"
    ],
    "keywords": [
      "mahler measure",
      "cm elliptic curves",
      "conductors",
      "functional equation",
      "conjectural relations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3036R"
    }
  }
}