{
  "abstract": "Let $π$ be a generic irreducible representation of $\\mathrm{GL}_n(\\mathbf{F})$ for a local field $\\mathbf{F}$. We introduce the Voronoi--Hankel transform $\\mathcal{VH}_π$ for $π$, and prove it is equivalent to the $π$-Fourier transform introduced by Jiang--Luo. We give an extension $\\widetilde{\\mathcal{VH}}_π$ of $\\mathcal{VH}_π$ to some larger class of functions on $\\mathbf{F}^{\\times}$, and prove the multiplicativity with respect to parabolic induction via the above-mentioned equivalence. For non-archimedean $\\mathbf{F}$ we give a systematical study of the relevant kernel function, including the asymptotic behavior at $0$ and $\\infty$, as well as some simple integral representation based on the local Langlands correspondences for the essentially tame supercuspidals. As an application in the non-archimedean case, we give an effective version of the stability theorem for the twisted local gamma factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04336",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhefeng Shen"
    },
    {
      "name": "Han Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3v4hr2ez20qtk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04336",
  "fulltext_url": null,
  "id": "3v4hr2ez20qtk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04336",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7163571842",
  "pdf_url": "https://arxiv.org/pdf/2606.04336",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3v4hr2ez20qtk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2606.04336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04336"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Voronoi-Hankel Transforms",
  "title_text": "Voronoi-Hankel Transforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3v4hr2ez20qtk",
  "venue": "arXiv",
  "versions": []
}