{
  "abstract": "For an integer $d\\ge 3$, put $Δ_d=\\min{2^{d-1},d(d-1)}$. Let $a/q$ be reduced, let $P(X)=\\frac{a}{q}X^d+α_{d-1}X^{d-1}+\\cdots+α_0$, and let $\\mathcal{I}$ be an interval of $H\\le q$ consecutive integers. We prove $\\left|\\sum_{n\\in\\mathcal{I}}e(P(n))\\right|\\ll_{d,\\varepsilon}q^{1/d}H^\\varepsilon+H^{1-1/Δ_d+\\varepsilon}$. Consequently, for every prime $p>d$, every degree-$d$ polynomial $P\\in\\mathbb{F}p[X]$, and every interval $\\mathcal{I}$ of $H$ consecutive integers with $p^{1/d}<H<p^{1/(d-1)}$, writing $H^d/p=H^u$, one has $\\left|\\sum{n\\in\\mathcal{I}}e_p(P(n))\\right|\\ll_{d,\\varepsilon}H^{1-\\min{u/d,1/Δ_d}+\\varepsilon}$. This strictly improves throughout the full natural short-interval window the best generic estimate obtained by combining classical Weyl differencing with the optimal Vinogradov mean value theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02478",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiyu Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fscvdk2cx45te.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02478",
  "fulltext_url": null,
  "id": "fscvdk2cx45te",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02478",
  "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"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7207770571",
  "pdf_url": "https://arxiv.org/pdf/2609.02478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fscvdk2cx45te.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Improved Weyl bounds on short intervals",
  "title_text": "Improved Weyl bounds on short intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/fscvdk2cx45te",
  "venue": "arXiv",
  "versions": []
}