{
  "id": "1207.0617",
  "version": "v5",
  "published": "2012-07-03T09:27:16.000Z",
  "updated": "2014-11-16T12:59:56.000Z",
  "title": "Algebraic twists of modular forms and Hecke orbits",
  "authors": [
    "Étienne Fouvry",
    "Emmanuel Kowalski",
    "Philippe Michel"
  ],
  "comment": "v5, final version to appear in GAFA",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on the ell-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-11-27T06:13:45.000Z",
      "comment": "v4, add references to new applications to sums over primes; some material in v3 that was not directly used but is needed for arXiv:1211.6043 is moved to that paper",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-11-16T12:59:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F32",
      "11F37",
      "11T23",
      "11L05"
    ],
    "keywords": [
      "modular forms",
      "algebraic twists",
      "ell-adic fourier transform",
      "fourier coefficients",
      "burgess type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0617F"
    }
  }
}