{
  "id": "1604.07664",
  "version": "v1",
  "published": "2016-04-26T13:08:14.000Z",
  "updated": "2016-04-26T13:08:14.000Z",
  "title": "Some applications of smooth bilinear forms with Kloosterman sums",
  "authors": [
    "Valentin Blomer",
    "Étienne Fouvry",
    "Emmanuel Kowalski",
    "Philippe Michel",
    "Djordje Milićević"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We revisit a recent bound of I. Shparlinski and T. P. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier results on sums of Kloosterman sums along the primes and on the error term of the fourth moment of Dirichlet $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-26T13:08:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11M06"
    ],
    "keywords": [
      "kloosterman sums",
      "smooth bilinear forms",
      "applications",
      "correlation sums",
      "fourier coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407664B"
    }
  }
}