{
  "abstract": "We construct a positive, finitely additive, left-invariant measure on the congruence cylinder ring of a smooth $d$-dimensional algebraic group over an $n$-dimensional local field. The measure takes values in $\\mathbb{R}((X_2))\\cdots((X_n))$. A normalized cylinder of depth $(i_1,\\ldots,i_n)$ has volume $q^{-di_1}\\prod_{\\ell=2}^nX_\\ell^{di_\\ell}$, where $q$ is the final residue-field cardinality. We also obtain coordinate-change and quotient integration formulas for this measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11468",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuecai Ma"
    },
    {
      "name": "Jingwen Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yp00g6ta1kpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11468",
  "fulltext_url": null,
  "id": "9yp00g6ta1kpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11468",
  "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": "W7221118588",
  "pdf_url": "https://arxiv.org/pdf/2610.11468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yp00g6ta1kpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Invariant Measures on Smooth Algebraic Groups over Higher Local Fields",
  "title_text": "Invariant Measures on Smooth Algebraic Groups over Higher Local Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/9yp00g6ta1kpc",
  "venue": "arXiv",
  "versions": []
}