{
  "id": "1108.2020",
  "version": "v2",
  "published": "2011-08-09T19:38:34.000Z",
  "updated": "2011-08-13T21:55:10.000Z",
  "title": "Logarithmic and absolute-value like properties of $π(x)$ with applications",
  "authors": [
    "Boris B. Benyaminov"
  ],
  "comment": "11 pages. Withdrawn by the author due to a problem with Theorem 3.1, thus also invalidating all results that were based on it",
  "categories": [
    "math.NT"
  ],
  "abstract": "We derive properties of $\\pi(x)$ reminiscent of those of the logarithm and absolute value functions. Two of these properties are similar to the relations defining the linearity of a function. Several applications of these properties of $\\pi(x)$ are also examined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-13T21:55:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41",
      "11M26"
    ],
    "keywords": [
      "applications",
      "logarithmic",
      "absolute-value",
      "absolute value functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2020B"
    }
  }
}