{
  "id": "0711.2240",
  "version": "v2",
  "published": "2007-11-14T16:19:48.000Z",
  "updated": "2007-11-19T19:57:45.000Z",
  "title": "A note on the least totient of a residue class",
  "authors": [
    "M. Z. Garaev"
  ],
  "comment": "Improved version",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $q$ be a large prime number, $a$ be any integer, $\\epsilon$ be a fixed small positive quantity. Friedlander and Shparlinksi \\cite{FSh} have shown that there exists a positive integer $n\\ll q^{5/2+\\epsilon}$ such that $\\phi(n)$ falls into the residue class $a \\pmod q.$ Here, $\\phi(n)$ denotes Euler's function. In the present paper we improve this bound to $n\\ll q^{2+\\epsilon}.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-19T19:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40"
    ],
    "keywords": [
      "residue class",
      "large prime number",
      "denotes eulers function",
      "fixed small positive quantity",
      "friedlander"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2240G"
    }
  }
}