{
  "abstract": "We prove a sharp effective equidistribution theorem for closed geodesics on a compact hyperbolic surface. This is achieved by carefully analyzing the Selberg trace formula twisted by a Maass eigenfunction, which we refer to as Zelditch's trace formula, following Zelditch's observation that the geometric side can be expressed as a sum of period integrals of eigenfunctions on closed geodesics. The main technical input is a sharp upper bound for the matrix coefficients $\\langle ϕ, φ^2 \\rangle$ uniformly in $t_ϕ\\to \\infty$ and $t_φ\\to \\infty$, where $t_ϕ$ and $t_φ$ are the eigenparameters corresponding to Maass forms $ϕ$ and $φ$ on $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27071",
  "author_total": 3,
  "authors": [
    {
      "name": "Junehyuk Jung"
    },
    {
      "name": "Insung Park"
    },
    {
      "name": "Peter Zenz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r7d56fvejjp3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27071",
  "fulltext_url": null,
  "id": "8r7d56fvejjp3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27071",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GT"
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      "arxiv",
      "math.SP"
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      "openalex",
      "2602|Analytic Number Theory Research"
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  "openalex": "W7214209005",
  "pdf_url": "https://arxiv.org/pdf/2609.27071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r7d56fvejjp3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp effective equidistribution of closed geodesics in compact hyperbolic surfaces",
  "title_text": "Sharp effective equidistribution of closed geodesics in compact hyperbolic surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/8r7d56fvejjp3",
  "venue": "arXiv",
  "versions": []
}