{
  "abstract": "Let $α$ be an element of $\\Fq((1/T))$ which is not in $\\Fq(T)$. We ask how small $\\nrm{απ}$ can be made when $π$ runs over irreducible polynomials, and write $θ(α)$ for the largest exponent $θ$ such that $\\nrm{απ}<|π|^{-θ}$ has infinitely many solutions. The analogue of Matomäki's exponent, $θ(α)\\ge\\frac13$, was proved by Baier and the author, and it is the natural limit of the Riemann Hypothesis. In this paper we go beyond it. For odd characteristic $p$ and $q$ large in terms of $p$ and $θ$, we prove that $θ(α)\\geθ$ for every $α$ and every $θ<\\sqrt2-1=0.414\\ldots$, and for every $θ<\\frac12$ when $α$ has bounded partial quotients. The main tools are an exact count of points in affine subspaces of $\\Fq[T]$, a splitting of these subspaces into long arithmetic progressions, and the results of Sawin and Shusterman on the Möbius function along such progressions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00623",
  "author_total": 1,
  "authors": [
    {
      "name": "Esrafil Ali Molla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bw4mtt54ftcmf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00623",
  "fulltext_url": null,
  "id": "bw4mtt54ftcmf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00623",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00623",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bw4mtt54ftcmf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00623",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00623"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The distribution of $απ$ modulo one in $\\Fq(T)$: beyond Matomäki's exponent",
  "title_text": "The distribution of απ modulo one in Fq(T): beyond Matomäki's exponent",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/bw4mtt54ftcmf",
  "venue": "arXiv",
  "versions": []
}