{
  "id": "1308.1037",
  "version": "v3",
  "published": "2013-08-05T16:49:01.000Z",
  "updated": "2014-10-15T20:30:19.000Z",
  "title": "Zagier duality and integrality for Fourier coefficients for weakly holomorphic modular forms",
  "authors": [
    "Yichao Zhang"
  ],
  "comment": "Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note, we generalize the isomorphisms to the case when the discriminant form is not necessarily induced from real quadratic fields. In particular, this general setting includes all the subspaces with epsilon-conditions, only two spacial cases of which were treated before. With this established, we shall prove the Zagier duality for canonical bases. Finally, we raise a question on the integrality of the Fourier coefficients of these bases elements, or equivalently we concern the existence of a Miller-like basis for vector valued modular forms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-03T15:17:12.000Z",
      "comment": "Worked out the isomorphisms for a general delta; proved Zagier duality for canonical bases; raise a question on integrality; 27 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-15T20:30:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F27"
    ],
    "keywords": [
      "weakly holomorphic modular forms",
      "fourier coefficients",
      "zagier duality",
      "integrality",
      "vector valued modular forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.1037Z"
    }
  }
}