{
  "id": "1901.07280",
  "version": "v1",
  "published": "2019-01-22T12:14:03.000Z",
  "updated": "2019-01-22T12:14:03.000Z",
  "title": "On the mean value of the magnitude of an exponential sum involving the divisor function",
  "authors": [
    "Mayank Pandey"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain tight bounds on the L^1 norm of the exponential sum $M(\\alpha) = \\sum_{n\\le X}\\tau(n)e(n\\alpha)$ where $\\tau(n) = \\sum_{d|n} 1$ is the divisor function. In particular, we show that it is $\\gg \\sqrt{X}\\log X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-22T12:14:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential sum",
      "divisor function",
      "mean value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}