{
  "abstract": "The Ramanujan bound states that the degree of the trace of the $\\mathfrak{p}$-Hecke operator on a space of weight $k$ Drinfeld cusp forms is at most $d(k-2)/2$, where $\\mathfrak{p}$ is a prime of degree $d$ in $\\mathbb{F}_q[T]$. We prove the strong Ramanujan bound, which states that at level 1, this bound can be improved to $d(k-(q+1))/2$. In addition, we classify when the strong Ramanujan bound is sharp; surprisingly, this turns out to depend on $\\mathfrak{p}$ only through the parity of its degree. We also prove results related to the smallest slope of the Atkin operator and mod $p$ distributions of Frobenius polynomials of Drinfeld modules over finite fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14458",
  "author_total": 1,
  "authors": [
    {
      "name": "Sjoerd de Vries"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgd0g2hdtg6ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14458",
  "fulltext_url": null,
  "id": "bgd0g2hdtg6ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14458",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221775309",
  "pdf_url": "https://arxiv.org/pdf/2610.14458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgd0g2hdtg6ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The strong Ramanujan bound for Drinfeld modular forms",
  "title_text": "The strong Ramanujan bound for Drinfeld modular forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bgd0g2hdtg6ev",
  "venue": "arXiv",
  "versions": []
}