{
  "abstract": "We identify the optimal constant and describe all maximizers for the Fourier endpoint extension inequality associated with the moment curve over finite fields. This confirms a conjecture proposed in the authors' earlier work. The proof proceeds by showing that the problem is equivalent to a purely probabilistic extremal statement: among all probability distributions on a finite set, the uniform distribution uniquely maximizes the expected number of distinct rearrangements of an i.i.d. sample.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29882",
  "author_total": 7,
  "authors": [
    {
      "name": "Chandan Biswas"
    },
    {
      "name": "Emanuel Carneiro"
    },
    {
      "name": "Taryn C. Flock"
    },
    {
      "name": "José Madrid"
    },
    {
      "name": "Diogo Oliveira e Silva"
    },
    {
      "name": "Betsy Stovall"
    },
    {
      "name": "James Tautges"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c765eygmyttac.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29882",
  "fulltext_url": null,
  "id": "c765eygmyttac",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29882",
  "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.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214345649",
  "pdf_url": "https://arxiv.org/pdf/2609.29882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c765eygmyttac.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution",
  "title_text": "Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/c765eygmyttac",
  "venue": "arXiv",
  "versions": []
}