{
  "abstract": "Let $n,k\\ge 2$ and $N_{n,k} = \\binom{n+k}{k}-1$. We prove that if $f \\in L^{p}(\\mathbb{R}^{N_{n,k}})$ and $\\hat{f}$ is supported on the $n$-dimensional Parsell-Vinogradov manifold, then $f \\equiv 0$ whenever $1\\le p < p_{c}(n,k) = n+ \\binom{n+k}{n+1}$. This improves the bound by Agranovsky and Narayanan, and generalizes the moment-curve result of Guo-Iosevich-Zhang-Zorin-Kranich. The exponent $p_{c}(n,k)$ is sharp when $n=2$ or $k=2$, since it matches the convergence exponent $p_{n,k}^{\\mathrm{Tar}}$ of Tarry's problem. Our result also yields a general lower bound $p_{n,k}^{\\mathrm{Tar}} \\ge p_{c}(n,k)$, improving Ikromov's bound by $n-1$. The proof combines the rotation symmetry of Parsell-Vinogradov manifold with the essential orthogonality of rotated covering boxes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39739",
  "author_total": 2,
  "authors": [
    {
      "name": "Cheng Bi"
    },
    {
      "name": "Ruichen Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnvpnapxtnmx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39739",
  "fulltext_url": null,
  "id": "fnvpnapxtnmx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39739",
  "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.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnvpnapxtnmx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39739"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^p$ integrability of functions with Fourier support on High codimension manifolds",
  "title_text": "L^p integrability of functions with Fourier support on High codimension manifolds",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fnvpnapxtnmx8",
  "venue": "arXiv",
  "versions": []
}