{
  "id": "1309.7467",
  "version": "v2",
  "published": "2013-09-28T15:22:56.000Z",
  "updated": "2013-11-12T16:19:53.000Z",
  "title": "Cuspidal part of an Eisenstein series restricted to an index 2 subfield",
  "authors": [
    "Yueke Hu"
  ],
  "comment": "Thesis",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathbb{E}$ be a quadratic extension of a number field $\\mathbb{F}$. Let $E(g, s)$ be an Eisenstein series on $GL_2(\\mathbb{E})$, and let $F$ be a cuspidal automorphic form on $GL_2(\\mathbb{F})$. We will consider in this paper the following automorphic integral: $$\\int_{Z_{A}GL_{2}(\\mathbb{F})\\backslash GL_{2}(\\mathbb{A}_{\\mathbb{F}})} F(g)E(g,s) dg.$$ This is in some sense the complementary case to the well-known Rankin-Selberg integral and the triple product formula. We will approach this integral by Waldspurger's formula. We will discuss when the integral is automatically zero, and otherwise the L-function it represents. We will calculate local integrals at some ramified places, where the level of the ramification can be arbitrarily large.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-12T16:19:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eisenstein series",
      "cuspidal part",
      "cuspidal automorphic form",
      "triple product formula",
      "well-known rankin-selberg integral"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7467H"
    }
  }
}