{
  "id": "1805.11319",
  "version": "v1",
  "published": "2018-05-29T09:17:02.000Z",
  "updated": "2018-05-29T09:17:02.000Z",
  "title": "Asymptotic Formulas Related to the $M_2$-rank of Partitions without Repeated Odd Parts",
  "authors": [
    "Chris Jennings-Shaffer",
    "Dillon Reihill"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give asymptotic expansions for the moments of the $M_2$-rank generating function and for the $M_2$-rank generating function at roots of unity. For this we apply the Hardy-Ramanujan circle method extended to mock modular forms. Our formulas for the $M_2$-rank at roots of unity lead to asymptotics for certain combinations of $N2(r,m,n)$ (the number of partitions without repeated odd parts of $n$ with $M_2$-rank congruent to $r$ modulo $m$). This allows us to deduce inequalities among certain combinations of $N2(r,m,n)$. In particular, we resolve a few conjectured inequalities of Mao.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T09:17:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "repeated odd parts",
      "asymptotic formulas",
      "partitions",
      "rank generating function",
      "hardy-ramanujan circle method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}