{
  "id": "1512.01191",
  "version": "v1",
  "published": "2015-12-03T19:03:56.000Z",
  "updated": "2015-12-03T19:03:56.000Z",
  "title": "A note on the Borwein conjecture",
  "authors": [
    "Jiyou Li"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "The Borwein conjecture asserts that for any positive integer $n$ and $k$, the coefficient $a_{3k}$ of $q^{3k}$ in the expansion of $\\prod_{j=0}^n (1-q^{3j+1})(1-q^{3j+2})$ is nonnegative. In this note we prove that for any $k\\leq n$, $$a_{3k}+a_{3(n+1)+3k}+\\cdots+a_{3n(n+1)+3k}>0.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T19:03:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "borwein conjecture asserts",
      "positive integer",
      "coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}