{
  "abstract": "For each integer $k\\ge3$, we establish the following estimate for all $1\\le p<\\infty$ and $\\varepsilon>0$: \\[ \\left\\|\\sup_{t\\in\\mathbb{T}}\\left|\\sum_{n=1}^N e(nx+n^kt)\\right|\\right\\|_{L^p(\\mathbb{T})} \\ll_{k,p,\\varepsilon} N^{\\max\\{1-1/K_k,\\,1-1/p\\}+\\varepsilon}, \\] where $K_k=\\min\\{2^{k-1},k(k+1)/2\\}$, $e(z)=e^{2πiz}$, and $\\mathbb{T}=\\mathbb{R}/\\mathbb{Z}$. For $k\\ge5$, this improves our earlier bound \\cite{chen-miao-yuan-zhao} for $1\\le p<D_k$, where $D_k=\\min\\{2^{k-1},k(k-1)\\}$, and, together with the corresponding lower bound, extends the sharp range up to $N^\\varepsilon$ from $p\\ge D_k$ to $p\\ge K_k$. The main new ingredient is a mixed minor-arc moment estimate obtained before taking the time supremum. The minor-arc maximal estimate then follows from a smooth reproducing kernel argument, while the major arcs are handled directly by Poisson summation and classical complete exponential-sum estimates. The reduction from suprema to mean values also yields a short and direct proof of improved $L^p$ estimates for maximal operators on Weyl sums with general polynomial phases, strengthening \\cite[Theorem 1.1]{baker-chen-shparlinski}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23379",
  "author_total": 4,
  "authors": [
    {
      "name": "Xuezhi Chen"
    },
    {
      "name": "Changxing Miao"
    },
    {
      "name": "Jiye Yuan"
    },
    {
      "name": "Tengfei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0ktw6hh9a31x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23379",
  "fulltext_url": null,
  "id": "e0ktw6hh9a31x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23379",
  "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"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222964196",
  "pdf_url": "https://arxiv.org/pdf/2610.23379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0ktw6hh9a31x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Improved $L^p$ maximal estimates for higher-degree Weyl sums",
  "title_text": "Improved L^p maximal estimates for higher-degree Weyl sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/e0ktw6hh9a31x",
  "venue": "arXiv",
  "versions": []
}