{
  "id": "1512.01128",
  "version": "v1",
  "published": "2015-12-01T08:38:53.000Z",
  "updated": "2015-12-01T08:38:53.000Z",
  "title": "A note on the exponential sums of the localized divisor functions",
  "authors": [
    "Giovanni Coppola",
    "Maurizio Laporta"
  ],
  "comment": "Four pages, Plain TeX",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an upper bound for the exponential sum associated to a localized $k-$divisor function, i.e., the counting function of the number of ways to write a positive integer $n$ as a product of $k\\ge 2$ positive integers, each of them belonging to a specified interval. In particular, this gives an estimate for the exponential sum for the $k-$divisor function, $d_k(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-01T08:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L07",
      "11N99"
    ],
    "keywords": [
      "exponential sum",
      "localized divisor functions",
      "positive integer",
      "upper bound",
      "counting function"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151201128C"
    }
  }
}