{
  "id": "1101.4557",
  "version": "v3",
  "published": "2011-01-24T14:58:40.000Z",
  "updated": "2012-05-05T05:44:24.000Z",
  "title": "On the counting function of sets with even partition functions",
  "authors": [
    "Fethi Ben Said",
    "Jean-Louis Nicolas"
  ],
  "journal": "Publ. Math. Debrecen 79, 3-4 (2011) 687-697",
  "doi": "10.5486/PMD.2011.5106",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let q be an odd positive integer and P \\in F2[z] be of order q and such that P(0) = 1. We denote by A = A(P) the unique set of positive integers satisfying \\sum_{n=0}^\\infty p(A, n) z^n \\equiv P(z) (mod 2), where p(A,n) is the number of partitions of n with parts in A. In [5], it is proved that if A(P, x) is the counting function of the set A(P) then A(P, x) << x(log x)^{-r/\\phi(q)}, where r is the order of 2 modulo q and \\phi is Euler's function. In this paper, we improve on the constant c=c(q) for which A(P,x) << x(log x)^{-c}.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-05T05:44:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "counting function",
      "partition functions",
      "eulers function",
      "unique set",
      "odd positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4557B"
    }
  }
}