{
  "id": "1607.01098",
  "version": "v1",
  "published": "2016-07-05T02:51:51.000Z",
  "updated": "2016-07-05T02:51:51.000Z",
  "title": "On the Fourier Transform of Bessel Functions over Complex Numbers - II: the General Case",
  "authors": [
    "Zhi Qi"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory of the relative trace formula for the Shimura-Waldspurger correspondence and extend the Waldspurger formula from totally real fields to arbitrary number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-05T02:51:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "33C10"
    ],
    "keywords": [
      "bessel functions",
      "complex numbers",
      "fourier transform",
      "general case",
      "radial exponential integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}