{
  "id": "1708.04197",
  "version": "v1",
  "published": "2017-08-14T16:16:53.000Z",
  "updated": "2017-08-14T16:16:53.000Z",
  "title": "On Drinfeld modular forms of higher rank II",
  "authors": [
    "Ernst-Ulrich Gekeler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that the absolute value $|f|$ of an invertible holomorphic function $f$ on the Drinfeld symmetric space $\\OM^r$ $(r \\geq 2)$ is constant on fibers of the building map to the Bruhat-Tits building $\\MB\\MT$. Its logarithm $\\log|f|$ is an affine map on the realization of $\\MB\\MT$. These results are used to study the vanishing loci of modular forms (coefficient forms, Eisenstein series, para-Eisenstein series) and to determine their images in $\\MB\\MT$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-14T16:16:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F52",
      "14G22"
    ],
    "keywords": [
      "drinfeld modular forms",
      "higher rank",
      "drinfeld symmetric space",
      "para-eisenstein series",
      "absolute value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}