{
  "id": "1805.09809",
  "version": "v1",
  "published": "2018-05-24T17:52:09.000Z",
  "updated": "2018-05-24T17:52:09.000Z",
  "title": "On Unfoldings of Some Integrals of Automorphic Functions on General Linear Groups",
  "authors": [
    "Eleftherios Tsiokos"
  ],
  "categories": [
    "math.NT",
    "math.GR",
    "math.RT"
  ],
  "abstract": "We use results about Fourier coefficients appearing in [T] (and some more obtained here), to obtain information for certain among the integrals of the form $$I=\\int_{GL_n(\\kkk)Z_n(\\A)\\s GL_n(\\A)}\\varphi(g)\\phi(g)\\F(E)(\\tj(g))dg$$ where: $\\A$ is the adele ring of a number field $\\kkk$; $\\varphi$ is a $GL_n(\\A)$-cuspidal automorphic form; $\\phi$ is a $GL_n(\\A)$-automorphic function (even the trivial for some results); $E$ is a $GL_{N}(\\A)$-automorphic form for a multiple $N$ of $n$; $\\F(E)$ is a Fourier coefficient of $E$ for certain choices of additive functions $\\F$ in a set $\\BBnk[N]$ which we defined in $[T];$ $\\tj$ is a diagonal embedding of $GL_n$ in $GL_N$; of course $\\tj(GL_n)\\in\\Stab{GL_N}{\\F}$; and $Z_n$ is the center of $GL_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-24T17:52:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear groups",
      "automorphic function",
      "unfoldings",
      "cuspidal automorphic form",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}