{
  "id": "1610.09171",
  "version": "v1",
  "published": "2016-10-28T11:23:25.000Z",
  "updated": "2016-10-28T11:23:25.000Z",
  "title": "On Kloosterman sums with multiplicative coefficients",
  "authors": [
    "M. A. Korolev"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The series of some new estimates for the sums of the type \\[ S_{q}(x;f)\\,=\\,\\mathop{{\\sum}'}\\limits_{n\\leqslant x}f(n)e_{q}(an^{*}+bn) \\] is obtained. Here $q$ is a sufficiently large integer, $\\sqrt{q}(\\log{q})\\!\\ll\\!x\\leqslant q$, $a,b$ are integers, $(a,q)=1$, $e_{q}(v) = e^{2\\pi iv/q}$, $f(n)$ is a multiplicative function, $nn^{*}\\equiv 1 \\pmod{q}$ and the prime sign means that $(n,q)=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-28T11:23:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05"
    ],
    "keywords": [
      "kloosterman sums",
      "multiplicative coefficients",
      "prime sign means",
      "sufficiently large integer",
      "multiplicative function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}