{
  "id": "math/0309023",
  "version": "v3",
  "published": "2003-09-01T14:27:50.000Z",
  "updated": "2004-12-22T17:16:59.000Z",
  "title": "A formula for the central value of certain Hecke L-functions",
  "authors": [
    "Ariel Pacetti"
  ],
  "comment": "43 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let N = 1 mod 4 be the negative of a prime, K=Q(sqrt{N}) and O_K its ring of integers. Let D be a prime ideal in O_K of prime norm congruent to 3 modulo 4. Under these assumptions, there exists Hecke characters $\\psi_{\\D}$ of K with conductor $(\\D)$ and infinite type $(1,0)$. Their L-series L(\\psi_\\D,s)$ are associated to a CM elliptic curve E(N,\\D) defined over the Hilbert class field of $K$. We will prove a Waldspurger-type formula for L(\\psi_\\D,s) of the form L(\\psi_\\D,1) = \\Omega \\sum_{[\\A],I} r(\\D,[\\A],I) m_{[\\A],I}([\\D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at |N| and infinity and [\\A] are class group representatives of $K$. An application of this formula for the case N=-7 will allow us to prove the non-vanishing of a family of L-series of level $7|D|$ over $K$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-12-22T17:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40"
    ],
    "keywords": [
      "central value",
      "hecke l-functions",
      "prime norm congruent",
      "prime ideal",
      "hecke characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9023P"
    }
  }
}