{
  "id": "2004.14244",
  "version": "v1",
  "published": "2020-04-29T14:48:33.000Z",
  "updated": "2020-04-29T14:48:33.000Z",
  "title": "Eulerianity of Fourier coefficients of automorphic forms",
  "authors": [
    "Dmitry Gourevitch",
    "Henrik P. A. Gustafsson",
    "Axel Kleinschmidt",
    "Daniel Persson",
    "Siddhartha Sahi"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "hep-th",
    "math.RT"
  ],
  "abstract": "We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-29T14:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F70",
      "22E55",
      "20G45"
    ],
    "keywords": [
      "automorphic forms",
      "parabolic fourier coefficients",
      "general transfer theorem",
      "next-to-minimal automorphic representations",
      "next-to-minimal representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}