{
  "abstract": "We solve the sup-norm problem for minimal weight vectors in an arbitrary cuspidal representation $π$ of $\\mathrm{GL}(n,\\mathbb{Z})\\backslash\\mathrm{GL}(n,\\mathbb{R})$ with a uniform power saving bound in terms of the archimedean data of $π$, including its spectral parameters and the dimension of its minimal $K$-type. As a key ingredient, we establish new uniform decay bounds for generalized spherical functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19121",
  "author_total": 4,
  "authors": [
    {
      "name": "Valentin Blomer"
    },
    {
      "name": "Gergely Harcos"
    },
    {
      "name": "Péter Maga"
    },
    {
      "name": "Djordje Milićević"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7wv2mzzw540z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19121",
  "fulltext_url": null,
  "id": "a7wv2mzzw540z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19121",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213528070",
  "pdf_url": "https://arxiv.org/pdf/2609.19121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7wv2mzzw540z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The non-spherical sup-norm problem for $\\mathrm{GL}(n)$ and generalized spherical functions",
  "title_text": "The non-spherical sup-norm problem for GL(n) and generalized spherical functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/a7wv2mzzw540z",
  "venue": "arXiv",
  "versions": []
}