{
  "abstract": "In this work, we establish the sharp $L^2 \\to L^4$ extension inequality for a large class of quadratic surfaces in $\\mathbb{F}^3$, where $\\mathbb{F}$ is a finite field of odd characteristic. These surfaces include the cones without the origin and the spheres with nonzero radius $j$ such that $-j$ is not a square in $\\mathbb{F}$. We also show that the maximizers of these inequalities must have constant modulus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13023",
  "author_total": 1,
  "authors": [
    {
      "name": "Pedro Ronda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4q1pzevrvnqse.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13023",
  "fulltext_url": null,
  "id": "4q1pzevrvnqse",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13023",
  "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"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212491563",
  "pdf_url": "https://arxiv.org/pdf/2609.13023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4q1pzevrvnqse.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp $L^2 \\to L^4$ extension inequality for quadratic surfaces in finite fields",
  "title_text": "Sharp L^2 → L^4 extension inequality for quadratic surfaces in finite fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/4q1pzevrvnqse",
  "venue": "arXiv",
  "versions": []
}