{
  "id": "math/0610360",
  "version": "v1",
  "published": "2006-10-11T09:59:05.000Z",
  "updated": "2006-10-11T09:59:05.000Z",
  "title": "The maximal order of a class of multiplicative arithmetical functions",
  "authors": [
    "László Tóth",
    "Eduard Wirsing"
  ],
  "journal": "Annales Univ. Sci. Budapest., Sect. Comp., 22 (2003), 353-364",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove simple theorems concerning the maximal order of a large class of multiplicative functions. As an application, we determine the maximal orders of certain functions of the type $\\sigma_A(n)= \\sum_{d\\in A(n)} d$, where A(n) is a subset of the set of all positive divisors of $n$, including the divisor-sum function $\\sigma(n)$ and its unitary and exponential analogues. We also give the minimal order of a new class of Euler-type functions, including the Euler-function $\\phi(n)$ and its unitary analogue.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-11T09:59:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11N37"
    ],
    "keywords": [
      "maximal order",
      "multiplicative arithmetical functions",
      "simple theorems",
      "euler-type functions",
      "minimal order"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10360T"
    }
  }
}