{
  "id": "1203.4647",
  "version": "v3",
  "published": "2012-03-21T03:55:52.000Z",
  "updated": "2012-06-15T02:46:59.000Z",
  "title": "Lower order terms for the moments of symplectic and orthogonal families of $L$-functions",
  "authors": [
    "Ian P. Goulden",
    "Duc Khiem Huynh",
    "Rishikesh",
    "Michael O. Rubinstein"
  ],
  "comment": "34 pages, 4 tables",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\\chi_d)$, and also of the $L$-functions associated to quadratic twists of an elliptic curve over $\\Q$. In so doing, we are led to study determinants of binomial coefficients of the form $\\det (\\binom{2k-i-\\lambda_{k-i+1}}{2k-2j})$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-15T02:46:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M50",
      "05E05"
    ],
    "keywords": [
      "lower order terms",
      "orthogonal families",
      "symplectic",
      "conjectured asymptotic expansions",
      "central point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.4647G"
    }
  }
}