{
  "id": "1104.3264",
  "version": "v2",
  "published": "2011-04-16T21:43:56.000Z",
  "updated": "2013-07-14T22:29:39.000Z",
  "title": "The distribution of totients",
  "authors": [
    "Kevin Ford"
  ],
  "comment": "very minor revision: Corrected statement of Lemma 7.2 and following comments",
  "journal": "(original version) Ramanujan J. 2 (1998), 67-151",
  "categories": [
    "math.NT"
  ],
  "abstract": "New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for V_k(x) (see the paragraph after (5.20)), fixed the statement and proof of Theorem 3. New, precise way to relate sums to volumes (Lemmas 3.1, 3.9) and provided full details in Section 6 of the proofs of Theorems 10-13. Slightly different versions of Theorems 10,11,12,14 (qualitatively the same) with simpler proofs. Sections 7 and 8 combined (new section 7). A few definitions, such as S-normal, changed slightly. Some reorganization of material.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-14T22:29:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distribution",
      "main results",
      "simpler proofs",
      "precise way",
      "relate sums"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3264F"
    }
  }
}