{
  "abstract": "Let $X=G/K$ be a symmetric space of noncompact type, of dimension $n$ and rank $r$, and let $Y=Γ\\backslash X$. Sarnak's local bound for an $L^2$-normalized spherical joint eigenfunction with regular tempered parameter of size $T$ is $\\|ϕ\\|_\\infty\\ll T^{(n-r)/2}$. We prove $o(T^{(n-r)/2})$ locally uniformly on every quotient. On finite-volume real hyperbolic manifolds this is uniform in the expanding cusp range $y\\leq T^β$, $β<1/2$. If the injectivity radius is bounded below, we prove the global estimate $T^{(n-r)/2}(\\log T)^{-r/2}$. The proof makes use of a novel kernel argument and a uniform bound on the spherical function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21580",
  "author_total": 1,
  "authors": [
    {
      "name": "Christopher Lutsko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bqch63b186g2k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21580",
  "fulltext_url": null,
  "id": "bqch63b186g2k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21580",
  "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.GT"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7204202409",
  "pdf_url": "https://arxiv.org/pdf/2608.21580",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqch63b186g2k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2608.21580",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21580"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Improved sup-norm bounds for locally symmetric spaces",
  "title_text": "Improved sup-norm bounds for locally symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/bqch63b186g2k",
  "venue": "arXiv",
  "versions": []
}