{
  "id": "2007.03489",
  "version": "v1",
  "published": "2020-07-07T14:24:03.000Z",
  "updated": "2020-07-07T14:24:03.000Z",
  "title": "Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms",
  "authors": [
    "Jan-Willem van Ittersum",
    "Georg Oberdieck",
    "Aaron Pixton"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko--Zagier differential equation for Jacobi forms. The transformation properties of the solutions under the Jacobi group are derived. A special feature of the solutions is the polynomial dependence of the index parameter. The results yield an explicit conjectural description for all double ramification cycle integrals in the Gromov--Witten theory of K3 surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-07T14:24:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gromov-witten theory",
      "k3 surfaces",
      "jacobi forms",
      "kaneko-zagier equation",
      "kaneko-zagier differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}