{
  "id": "2006.15511",
  "version": "v1",
  "published": "2020-06-28T05:07:48.000Z",
  "updated": "2020-06-28T05:07:48.000Z",
  "title": "3-Divisibility of 9- and 27-Regular Partitions",
  "authors": [
    "Sarma Abinash"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A partition of $n$ is $l$-regular if none of its parts is divisible by $l$. Let $b_l(n)$ denote the number of $l$-regular partitions of $n$. In this paper, using the theory of Hecke eigenforms explored by J.-P. Serre, we establish exact criteria for the $3$-divisibility of $b_9(n)$ and $b_{27}(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-28T05:07:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke eigenforms",
      "establish exact criteria",
      "regular partitions",
      "divisibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}