{
  "id": "1202.0729",
  "version": "v2",
  "published": "2012-02-03T15:11:46.000Z",
  "updated": "2012-04-05T09:55:24.000Z",
  "title": "Small values of the Euler function and the Riemann hypothesis",
  "authors": [
    "Jean-Louis Nicolas"
  ],
  "journal": "Acta Arithmetica, 155.3, 2012, 311--321",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\vfi$ be Euler's function, $\\ga$ be Euler's constant and $N_k$ be the product of the first $k$ primes. In this article, we consider the function $c(n) =(n/\\vfi(n)-e^\\ga\\log\\log n)\\sqrt{\\log n}$. Under Riemann's hypothesis, it is proved that $c(N_k)$ is bounded and explicit bounds are given while, if Riemann's hypothesis fails, $c(N_k)$ is not bounded above or below.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-05T09:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11M26"
    ],
    "keywords": [
      "euler function",
      "riemann hypothesis",
      "small values",
      "riemanns hypothesis fails",
      "eulers constant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0729N"
    }
  }
}