{
  "abstract": "We prove an $L^4$ Strichartz estimate for the dispersion $n_1^2+αn_2^2$ on $\\mathbb T^2$, for every $α>0$. The loss is controlled by the Shannon entropy of the normalized squared Fourier coefficients and the cardinality of their support $S$. In particular, we obtain a norm loss of $(\\log\\#S)^{1/2}$ on fixed time intervals, with constants locally uniform in $α$. This provides an irrational-dispersion counterpart of the cardinality estimate of Herr and Kwak [Forum Math. Pi (2024)] and improves the $N^\\varepsilon$ loss of Bourgain and Demeter [Ann. of Math. (2015)] to $(\\log N)^{1/2}$ on frequency boxes. The proof combines weighted incidence estimates, smooth localization, and an entropy recursion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09689",
  "author_total": 2,
  "authors": [
    {
      "name": "Ming Wang"
    },
    {
      "name": "Yuanjia Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/422zm27cbckdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09689",
  "fulltext_url": null,
  "id": "422zm27cbckdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09689",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7221034515",
  "pdf_url": "https://arxiv.org/pdf/2610.09689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/422zm27cbckdd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strichartz estimates on two-dimensional irrational tori",
  "title_text": "Strichartz estimates on two-dimensional irrational tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/422zm27cbckdd",
  "venue": "arXiv",
  "versions": []
}