{
  "abstract": "Let $\\text{F}$ be a non-archimedean local field of characteristic zero with residual characteristic $p$. In this paper, we study local converse theorems for $k$-middle supercuspidal representations of $\\text{GL}(kn, \\text{F})$ via explicit computations of twisted gamma factors on the Galois side, under the assumptions $p \\nmid kn$ and $q_{\\text{F}}>(k-1)^2$. Our results provide further evidence for a conjecture of the third-named author and Stevens on depth bounds for the twisting representations in the local converse theorem. For odd $k \\ge 3$, we obtain infinitely many families of supercuspidal representations for which the bound $\\left\\lfloor \\frac{kn}{2} \\right\\rfloor$ in the local converse theorem is not sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24918",
  "author_total": 3,
  "authors": [
    {
      "name": "Moshe Adrian"
    },
    {
      "name": "Michael Horzepa"
    },
    {
      "name": "David C. Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4m1zqyrsyvbba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24918",
  "fulltext_url": null,
  "id": "4m1zqyrsyvbba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24918",
  "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": "W7223036404",
  "pdf_url": "https://arxiv.org/pdf/2610.24918",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4m1zqyrsyvbba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24918"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local Converse Theorems for $k$-Middle Supercuspidal Representations of $p$-adic $\\text{GL}(kn)$",
  "title_text": "Local Converse Theorems for k-Middle Supercuspidal Representations of p-adic GL(kn)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4m1zqyrsyvbba",
  "venue": "arXiv",
  "versions": []
}