{
  "id": "1212.1864",
  "version": "v2",
  "published": "2012-12-09T07:42:07.000Z",
  "updated": "2014-04-27T09:04:09.000Z",
  "title": "On a generalization of arithmetic functions and the Ramanujan sums",
  "authors": [
    "Yusuke Fujisawa"
  ],
  "comment": "This paper has been withdrawn. The author noticed that this paper was not good",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a number field. This paper considers arithmetic functions over $K$, that are, complex valued functions on the set of nonzero integral ideals in $K$. Firstly we generalize some basic results on arithmetic functions. Next we define the generalized Ramanujan sums over $K$ and show some properties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-27T09:04:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11L26"
    ],
    "keywords": [
      "arithmetic functions",
      "generalization",
      "nonzero integral ideals",
      "number field",
      "generalized ramanujan sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.1864F"
    }
  }
}