{
  "id": "1711.09736",
  "version": "v1",
  "published": "2017-11-27T15:05:50.000Z",
  "updated": "2017-11-27T15:05:50.000Z",
  "title": "On Drinfeld modular forms of higher rank III: The analogue of the k/12-formula",
  "authors": [
    "Ernst-Ulrich Gekeler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Continuing the work of \\cite{7} and \\cite{8}, we derive an analogue of the classical \"$k/12$-formula\" for Drinfeld modular forms of rank $r \\geq 2$. Here the vanishing order $\\nu_{\\omega}(f)$ of one modular form at some point $\\omega$ of the complex upper half-plane is replaced by the intersection multiplicity $\\nu_{\\bo}(f_1,\\ldots,f_{r-1})$ of $r-1$ independent Drinfeld modular forms at some point $\\bo$ of the Drinfeld symmetric space $\\OM^r$. We apply the formula to determine the common zeroes of $r-1$ consecutive Eisenstein series $E_{q^{i}-1}$, where $n-r<i<n$ for some $n \\geq r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-27T15:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F52",
      "11G09"
    ],
    "keywords": [
      "higher rank",
      "independent drinfeld modular forms",
      "drinfeld symmetric space",
      "complex upper half-plane",
      "intersection multiplicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}