{
  "id": "2206.06798",
  "version": "v1",
  "published": "2022-06-14T12:42:18.000Z",
  "updated": "2022-06-14T12:42:18.000Z",
  "title": "On the common zeros of quasi-modular forms for $Γ_0^+(N)$ of level $N=1,2,3$",
  "authors": [
    "Bo-Hae Im",
    "Hojin Kim",
    "Wonwoong Lee"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study common zeros of the iterated derivatives of the Eisenstein series for $\\Gamma_0^+(N)$ of level $N=1,2$ and $3$, which are quasi-modular forms. More precisely, we investigate the common zeros of quasi-modular forms, and prove that all the zeros of the iterated derivatives of the Eisenstein series $\\frac{d^m E_k^{(N)}(\\tau)}{d\\tau^m}$ of weight $k=2,4,6$ for $\\Gamma_0^+(N)$ of level $N=2,3$ are simple by generalizaing the results of Meher \\cite{MEH} and Gun and Oesterl\\'{e} \\cite{SJ20} for SL$_2(\\mathbb{Z})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-14T12:42:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F99"
    ],
    "keywords": [
      "quasi-modular forms",
      "eisenstein series",
      "iterated derivatives",
      "study common zeros"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}