{
  "id": "math/0002103",
  "version": "v1",
  "published": "2000-02-13T15:44:18.000Z",
  "updated": "2000-02-13T15:44:18.000Z",
  "title": "Asymptotic density and the asymptotics of partition functions",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "17 pages. To appear in Acta Math. Hungarica",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the partition function of A. Let c = \\pi \\sqrt(2/3). Let \\alpha > 0. It is proved that log p_A(n) ~ c\\sqrt(\\alpha n) if and only if the set A has asymptotic density \\alpha.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-13T15:44:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P82",
      "11P70",
      "11B05"
    ],
    "keywords": [
      "asymptotic density",
      "partition function",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2103N"
    }
  }
}