{
  "id": "math/0301115",
  "version": "v1",
  "published": "2003-01-11T15:55:37.000Z",
  "updated": "2003-01-11T15:55:37.000Z",
  "title": "Central value of automorphic $L-$functions",
  "authors": [
    "Ehud Moshe Baruch",
    "Zhengyu Mao"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We prove a generalization to the totally real field case of the Waldspurger's formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger's formula in terms of equality between global distributions. As applications we generalize the Kohnen-Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindelof hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-11T15:55:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F37",
      "11F67"
    ],
    "keywords": [
      "central value",
      "half integral weight form",
      "waldspurgers formula",
      "automorphic",
      "totally real field case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1115M"
    }
  }
}