{
  "abstract": "Let $\\mathrm{GL}_n(\\mathbb{F}_q)$ be the group of $n\\times n$ invertible matrices over a finite field $\\mathbb{F}_q$. How many matrices in $\\mathrm{GL}_n(\\mathbb{F}_q)$ are there with a subset of their entries prescribed? Motivated by the random matrix theory of classical compact groups, we address this question and various variants, with a focus on asymptotic results that are valid as $n$ tends to infinity. Our methods are Fourier-analytic, with the main input being an exponential sum over $\\mathrm{GL}_n(\\mathbb{F}_q)$, evaluated in 1955 by Hodges via elementary methods. Our results turn out to be related to investigations carried out in other fields, including coding theory, universality for $p$-adic matrices and algebraic combinatorics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29305",
  "author_total": 1,
  "authors": [
    {
      "name": "Ofir Gorodetsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9r21tsdsmzz5x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29305",
  "fulltext_url": null,
  "id": "9r21tsdsmzz5x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29305",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223235350",
  "pdf_url": "https://arxiv.org/pdf/2610.29305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9r21tsdsmzz5x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Statistics of entries of matrices from the general linear group over a finite field",
  "title_text": "Statistics of entries of matrices from the general linear group over a finite field",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9r21tsdsmzz5x",
  "venue": "arXiv",
  "versions": []
}