{
  "id": "2206.02167",
  "version": "v1",
  "published": "2022-06-05T12:49:47.000Z",
  "updated": "2022-06-05T12:49:47.000Z",
  "title": "Asymptotic formula for the $M_2$-ranks of overpartitions",
  "authors": [
    "Helen W. J. Zhang",
    "Ying Zhong"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let $\\overline{N}_2(a,c,n)$ be the number of overpartitions of $n$ whose the $M_2$-rank is congruent to $a$ modulo $c$. In this paper, we obtain the asymptotic formula of $\\overline{N}_2(a,c,n)$ utilizing the Ingham Tauberian Theorem. As applications, we derive inequalities concerning with $\\overline{N}_2(a,c,n)$ including its strict concavity and log-concavity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-05T12:49:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P72",
      "11P82"
    ],
    "keywords": [
      "asymptotic formula",
      "overpartitions",
      "ingham tauberian theorem",
      "strict concavity",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}