{
  "abstract": "We use the Selberg zeta function to analyze the limiting behavior of resonances in a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated with the relevant non-Archimedean Schottky group acting on the Berkovich projective line.\n\nTo reveal more interesting and intricate structures of resonances, we introduce intermediate zeta functions that encapsulate both Archimedean and non-Archimedean information – whereas the classical Selberg and Ihara zeta functions reflect only Archimedean and non-Archimedean properties, respectively. As an application of our techniques, we derive an exponential error term in a result of McMullen (recently extended by Dang–Mehmeti) concerning the asymptotic vanishing rate of the Hausdorff dimension of limit sets of certain degenerating Schottky groups generating symmetric three-funnel surfaces.",
  "abstract_shown": true,
  "affiliations": [
    "Fudan University",
    "CNRS-Centre de Mathématiques Laurent Schwartz, École Polytechnique",
    "Department of Mathematics, University of Toronto",
    "Institut des Hautes Études Scientifiques"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jialun Li",
      "orcid": "0000-0002-8034-2910"
    },
    {
      "affs": [
        1
      ],
      "name": "Carlos Matheus",
      "orcid": "0000-0001-5119-9687"
    },
    {
      "affs": [
        2
      ],
      "name": "Wenyu Pan",
      "orcid": "0000-0001-8333-9074"
    },
    {
      "affs": [
        3
      ],
      "name": "Zhongkai Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv6yky2370526.bib",
  "cited_by": 0,
  "doi": "10.1017/fms.2026.10279",
  "fulltext_url": null,
  "id": "dv6yky2370526",
  "issns": [
    "2050-5094"
  ],
  "landing_url": "https://www.cambridge.org/core/product/identifier/S2050509426102795/type/journal_article",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/dv6yky2370526.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:37Z",
      "native_id": "10.1017/fms.2026.10279",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102795/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Selberg, Ihara and Berkovich",
  "title_text": "Selberg, Ihara and Berkovich",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T12:20:56Z",
  "url": "https://research.draconitic.com/paper/dv6yky2370526",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}