{
  "id": "1001.4496",
  "version": "v2",
  "published": "2010-01-25T18:34:33.000Z",
  "updated": "2011-07-31T13:08:18.000Z",
  "title": "Modular equations and lattice sums",
  "authors": [
    "Mathew Rogers",
    "Boonrod Yuttanan"
  ],
  "comment": "12 pages, Rewritten and updated",
  "categories": [
    "math.NT"
  ],
  "abstract": "We highlight modular equations discovered by Somos and Ramanujan, and use them to prove new relations between lattice sums and hypergeometric functions. We also discuss progress towards solving Boyd's Mahler measure conjectures, and we conjecture a new formula for $L(E,2)$ of conductor 17 elliptic curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-31T13:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "11F11",
      "65B10"
    ],
    "keywords": [
      "lattice sums",
      "solving boyds mahler measure conjectures",
      "highlight modular equations",
      "hypergeometric functions",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.4496R"
    }
  }
}