{
  "id": "1901.04835",
  "version": "v1",
  "published": "2019-01-06T16:44:32.000Z",
  "updated": "2019-01-06T16:44:32.000Z",
  "title": "Further Results on Vanishing Coefficients in Infinite Product Expansions",
  "authors": [
    "James Mc Laughlin"
  ],
  "comment": "8 pages",
  "journal": "J. Aust. Math. Soc. 98 (2015), no. 1, 69-77",
  "doi": "10.1017/S1446788714000536",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \\begin{equation*} \\frac{(q^{r-tk}, q^{mk-(r-tk)}; q^{mk})_\\infty}{(q^r,q^{mk-r}; q^{mk})_\\infty} =: \\sum_{n=0}^\\infty c_nq^n, \\end{equation*} for certain integers $k$, $m$ $s$ and $t$, where $r=sm+t$, then $c_{kn-rs}$ is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms of integer partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-06T16:44:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "33D15",
      "05A19"
    ],
    "keywords": [
      "infinite product expansions",
      "vanishing coefficients",
      "series expansions",
      "integer partitions",
      "simpler reformulation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}