{
  "abstract": "We prove sub-Riemannian Selberg trace formulae for compact quotients of SL(2,R). Using the Fourier decomposition along the SO(2)-fibers, we reduce the heat trace computation to the Selberg trace formula for Maass Laplacians on the hyperbolic plane. The resulting formula has an identity contribution and a hyperbolic contribution, the latter involving a theta factor that records both the twisting character and the central sign of the chosen lift to SL(2,\\mathbb R)). We then use this trace formula to compute the zeta-regularized determinant of the sub-Laplacian. The determinant formula is expressed as a universal factor depending only on the base hyperbolic surface times an explicit lift- and character-dependent Selberg-type product.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11813",
  "author_total": 1,
  "authors": [
    {
      "name": "Fabrice Baudoin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27aa84r0k77c0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11813",
  "fulltext_url": null,
  "id": "27aa84r0k77c0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11813",
  "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.DG"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7164350412",
  "pdf_url": "https://arxiv.org/pdf/2606.11813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27aa84r0k77c0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.11813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sub-Riemannian Selberg Trace Formulae for Compact Quotients of SL(2,R) and Determinants of Sub-Laplacians",
  "title_text": "Sub-Riemannian Selberg Trace Formulae for Compact Quotients of SL(2,R) and Determinants of Sub-Laplacians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/27aa84r0k77c0",
  "venue": "arXiv",
  "versions": []
}