{
  "id": "2009.01622",
  "version": "v1",
  "published": "2020-09-03T12:43:32.000Z",
  "updated": "2020-09-03T12:43:32.000Z",
  "title": "On Drinfeld modular forms of higher rank V: The behavior of distinguished forms on the fundamental domain",
  "authors": [
    "Ernst-Ulrich Gekeler"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "\\begin{document} \\begin This paper continues work of the earlier articles with the same title. For two classes of modular forms $f$: \\begin{itemize} \\item para-Eisenstein series $\\alpha_{k}$ and \\item coefficient forms ${}_a \\ell_{k}$, where $k \\in \\mathbb{N}$ and $a$ is a non-constant element of $\\mathbb{F}_{q}[T]$, \\end{itemize} the growth behavior on the fundamental domain and the zero loci $\\Omega(f)$ as well as their images $\\mathcal{BT}(f)$ in the Bruhat-Tits building $\\mathcal{BT}$ are studied. We obtain a complete description for $f = \\alpha_{k}$ and for those of the forms ${}_{a}\\ell_{k}$ where $k \\leq \\deg a$. It turns out that in these cases, $\\alpha_{k}$ and ${}_{a}\\ell_{k}$ are strongly related, e.g., $\\mathcal{BT}({}_{a}\\ell_{k}) = \\mathcal{BT}(\\alpha_{k})$, and that $\\mathcal{BT}(\\alpha_{k})$ is the set of $\\mathbb{Q}$-points of a full subcomplex of $\\mathcal{BT}$ with nice properties. As a case study, we present in detail the outcome for the forms $\\alpha_{2}$ in rank 3. \\end{abstract} \\maketitle \\end{document}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-03T12:43:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F52",
      "11F23",
      "11F85",
      "14G22"
    ],
    "keywords": [
      "drinfeld modular forms",
      "fundamental domain",
      "higher rank",
      "distinguished forms",
      "paper continues work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}