{
  "id": "1609.06184",
  "version": "v1",
  "published": "2016-09-20T14:04:49.000Z",
  "updated": "2016-09-20T14:04:49.000Z",
  "title": "On the Riesz means of $δ_k(n)$",
  "authors": [
    "Saurabh Kumar Singh"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k\\geq 1$ be an integer. Let $\\delta_k(n)$ denote the maximum divisor of $n$ which is co-prime to $k$. We study the error term of the general $m$-th Riesz mean of the arithmetical function $\\delta_k(n)$ for any positive integer $m \\ge 1$, namely the error term $E_m(x)$ where \\[ \\frac{1}{m!}\\sum_{n \\leq x}\\delta_k(n) \\left( 1-\\frac{n}{x} \\right)^m = M_{m, k}(x) + E_{m, k}(x). \\] We establish a non-trivial upper bound for $\\left | E_{m, k} (x) \\right |$, for any integer $m\\geq 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-20T14:04:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "error term",
      "non-trivial upper bound",
      "th riesz mean",
      "maximum divisor",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}