{
  "id": "math/0606762",
  "version": "v1",
  "published": "2006-06-29T15:06:32.000Z",
  "updated": "2006-06-29T15:06:32.000Z",
  "title": "Computation of central value of quadratic twists of modular L-functions",
  "authors": [
    "Zhengyu Mao",
    "Fernando Rodriguez-Villegas",
    "Gonzalo Tornaría"
  ],
  "comment": "13 pages; to appear in \"Ranks of elliptic curves and random matrix theory.\" (2005)",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let f be a newform of weight two, prime level p. If D is a fundamental discriminant, define the twisted L-function L(f,D,s) to be the L-function associated to the twist of f by the quadratic character of conductor D. In this paper we consider the question of computing the family of twisted central values {L(f,D,1) : |D| <= x} for some x, by using an explicit version of Waldspurger's formula relating the central values L(f,D,1) to the |D|-th Fourier coefficient of weigth 3/2 modular forms in Shimura correspondence with f.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-29T15:06:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F37",
      "11F67"
    ],
    "keywords": [
      "quadratic twists",
      "modular l-functions",
      "computation",
      "fundamental discriminant",
      "quadratic character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6762M"
    }
  }
}