{
  "abstract": "We show that any convex co-compact hyperbolic surface with exponent of convergence of Poincaré series $δ\\in (\\frac25,\\frac{14}{27})$ has an essential spectral gap of size $β=\\tfrac78(\\tfrac12-δ)+\\tfrac{1}{32}δ-ε$ for any $ε>0$. In particular, for $δ=\\frac12$ this becomes $β=\\tfrac{1}{64}-ε$. We show existence of the gap by proving a new Fractal Uncertainty Principle, using a two-ends Furstenberg theorem of O'Regan-Wu-Yi [arXiv:2607.08461].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30261",
  "author_total": 2,
  "authors": [
    {
      "name": "Alex Cohen"
    },
    {
      "name": "Semyon Dyatlov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ery2aynvdpnta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30261",
  "fulltext_url": null,
  "id": "ery2aynvdpnta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30261",
  "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.AP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214388693",
  "pdf_url": "https://arxiv.org/pdf/2609.30261",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ery2aynvdpnta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30261",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30261"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A 1/64 spectral gap for surfaces with $δ=1/2$",
  "title_text": "A 1/64 spectral gap for surfaces with δ=1/2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/ery2aynvdpnta",
  "venue": "arXiv",
  "versions": []
}