{
  "abstract": "Let $F$ be a $p$-adic field, let $k,c\\ge1$, and let $ρ$ be a $(k,c)$ representation of $\\mathrm{GL}_{kc}(F)$: a complex representation of finite length whose wave front set has $(k^c)$ as its unique maximal orbit, and which admits a $(k,c)$ functional that is unique up to scaling. We prove that the functions in the $(k,c)$ model of $ρ$ are of moderate growth, by relating this model to the Zelevinsky model of $ρ$, and obtain as a consequence a bound for the restriction of these functions to the standard Levi subgroup associated with the composition $(c^k)$ of $kc$. As applications, we study convergence problems of several integrals involving $(k,c)$ models: integrals from the generalized doubling method, and a new family of integrals which extends the Rankin--Selberg integrals for Speh representations of Lapid and Mao.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14744",
  "author_total": 1,
  "authors": [
    {
      "name": "Eyal Kaplan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k22z9r0nhb67.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14744",
  "fulltext_url": null,
  "id": "8k22z9r0nhb67",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14744",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221833124",
  "pdf_url": "https://arxiv.org/pdf/2610.14744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8k22z9r0nhb67.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bounds for (k,c) model functions over p-adic fields",
  "title_text": "Bounds for (k,c) model functions over p-adic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8k22z9r0nhb67",
  "venue": "arXiv",
  "versions": []
}