{
  "abstract": "Let $A=\\mathbb{F}_q[T]$ and $K=\\mathbb{F}_q(T)$, and let $ϕ$ be a Drinfeld $A$-module over $K$ of rank $r\\geq 2$. We study the reduction of $ϕ$ at primes $\\mathfrak{p} \\in A$ lying in a prescribed arithmetic progression, for which $ϕ(\\mathbb{F}_{\\mathfrak{p}})$ has at most $r-1$ cyclic components. We obtain asymptotic formulas for the number of such primes of a given degree, with error bounds uniform in the modulus of the arithmetic progression. Furthermore, when $\\mathrm{End}_{\\overline K}(ϕ)=A$, we sharpen the error term and, under additional hypotheses, establish a necessary and sufficient condition for positivity of the resulting density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03607",
  "author_total": 3,
  "authors": [
    {
      "name": "Prassanna Nand Jha"
    },
    {
      "name": "Arnab Saha"
    },
    {
      "name": "Akshaa Vatwani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8vp580b0wcdp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03607",
  "fulltext_url": null,
  "id": "f8vp580b0wcdp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03607",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8vp580b0wcdp.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cyclicity of Drinfeld modules modulo primes in arithmetic progressions",
  "title_text": "Cyclicity of Drinfeld modules modulo primes in arithmetic progressions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/f8vp580b0wcdp",
  "venue": "arXiv",
  "versions": []
}