{
  "id": "1005.4708",
  "version": "v3",
  "published": "2010-05-25T21:47:17.000Z",
  "updated": "2013-07-10T17:33:01.000Z",
  "title": "Oscillations in Mertens Theorems and Other Finite Sums and Products",
  "authors": [
    "N. A. Carella"
  ],
  "comment": "Improved Version, 14 Pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums of the reciprocal of the primes up to a fixed number and other finite sums and products are also given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-10T17:33:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11L20",
      "11N05"
    ],
    "keywords": [
      "finite sums",
      "mertens theorems",
      "note simplifies",
      "martens theorem",
      "error term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4708C"
    }
  }
}