{
  "abstract": "We extend the classical trace Paley-Wiener theorem for $p$-adic reductive groups, given by Bernstein, Deligne and Kazhdan in 1986, to a relative case. That is when $E/F$ is a quadratic extension of $p$-adic fields, the main result is a scalar Paley-Wiener theorem for relative Bessel distributions on $\\mathrm{GL}_n(F)\\backslash \\mathrm{GL}_n(E)$. These distributions are relative character of the form $$π\\mapsto I_π(f), \\ f\\in C_c^\\infty(\\mathrm{GL}_n(E)),$$ as $π$ ranges over $\\mathrm{GL}_n(F)$-distinguished irreducible tempered representations, and are constructed from a $\\mathrm{GL}_n(F)$-invariant functional and a Whittaker functional. Using the local Langlands correspondence, and the base-change from a unitary group, we show that the relative characters can be described as elements of the \"generic\" Bernstein center of the unitary group $U(n)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15432",
  "author_total": 1,
  "authors": [
    {
      "name": "Juliette Coutens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0eb4xms9d1rdb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15432",
  "fulltext_url": null,
  "id": "0eb4xms9d1rdb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15432",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221766288",
  "pdf_url": "https://arxiv.org/pdf/2610.15432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0eb4xms9d1rdb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15432"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A trace Paley-Wiener theorem for $\\mathrm{GL}_{n}(F)\\backslash \\mathrm{GL}_{n}(E)$, with $E/F$ a quadratic extension of non-Archimedean local fields",
  "title_text": "A trace Paley-Wiener theorem for GL_n(F)backslash GL_n(E), with E/F a quadratic extension of non-Archimedean local fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0eb4xms9d1rdb",
  "venue": "arXiv",
  "versions": []
}