{
  "id": "1601.06674",
  "version": "v1",
  "published": "2016-01-25T17:00:58.000Z",
  "updated": "2016-01-25T17:00:58.000Z",
  "title": "The $M_2$-rank of partitions without repeated odd parts as a harmonic Maass form",
  "authors": [
    "Chris Jennings-Shaffer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "While it is known that the $M_2$-rank of partitions without repeated odd parts is the so-called holomorphic part of a certain harmonic Maass form, much more can been done with this fact. We greatly improve the standing of this function as a harmonic Maass form, in particular we show the related harmonic Maass form transforms like the generating function for partitions without repeated odd parts (which is a modular form). We then use these improvements to determine formulas for the rank differences modulo $7$. Additionally we give identities and formulas that allow one to determine formulas for the rank differences modulo $c$, for any $c>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-25T17:00:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "repeated odd parts",
      "rank differences modulo",
      "partitions",
      "determine formulas",
      "related harmonic maass form transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106674J"
    }
  }
}