{
  "abstract": "We answer a question of C. S. Herz about the number of integral $k\\times m$ matrices $T$ such that $T^tT\\leq R$ for a fixed positive definite $m\\times m$ matrix $R$. We give an asymptotic formula for the count. This can be seen as a generalization of the Gauss circle problem, as counting representation of quadratic forms by the identity $I_k$, and as counting integral points bounded by the Stiefel manifold $T^tT=R$. The main tool is a bound for Bessel functions of matrix argument that was proved over Jordan algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07133",
  "author_total": 1,
  "authors": [
    {
      "name": "Gilles Felber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91r9m8mdc74tr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07133",
  "fulltext_url": null,
  "id": "91r9m8mdc74tr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07133",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212064473",
  "pdf_url": "https://arxiv.org/pdf/2609.07133",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91r9m8mdc74tr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07133"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counting Representations of Quadratic Forms",
  "title_text": "Counting Representations of Quadratic Forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/91r9m8mdc74tr",
  "venue": "arXiv",
  "versions": []
}