{
  "id": "2211.10644",
  "version": "v1",
  "published": "2022-11-19T10:16:25.000Z",
  "updated": "2022-11-19T10:16:25.000Z",
  "title": "A Generalisation of Euler Totient Function",
  "authors": [
    "Vlad Robu"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Euler's totient function, $\\varphi(n)$, which counts how many of $0,1,\\dots,n-1$ are coprime to $n$, has an explicit asymptotic lower bound of $n/\\log \\log n$, modulo some constant. In this note, we generalise $\\varphi$; given an irreducible integer polynomial $P$, we define the arithmetic function $\\varphi_P(n)$ that counts the amount of numbers among $P(0),P(1),\\dots,P(n-1)$ that are coprime to $n$. We also provide an asymptotic lower bound for $\\varphi_P(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-19T10:16:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "11N37"
    ],
    "keywords": [
      "euler totient function",
      "generalisation",
      "explicit asymptotic lower bound",
      "eulers totient function",
      "arithmetic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}