{
  "abstract": "Let $k\\geq 3$ be a fixed integer and $x$ be a large real number. Let $0<c_0<θ\\leq 1$ be a fixed real number for some $c_0>0.$ In this paper we show that there exists a constant $1/2\\leq δ_k(θ)<1$ such that the interval $[x, x + x^{δ_k(θ) +\\varepsilon} ]$ contains an integer of the form $n_1n_2 \\cdots n_k$ such that $|n_j-n^{1/k}|\\ll n^{θ/k} \\ (j=1,2, \\cdots, k)$. Especially we have $δ_3(1) = δ_4(1) = 1/2,$ which improves previous results of Chan.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00386",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenguang Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f03rz3jxhkhrr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00386",
  "fulltext_url": null,
  "id": "f03rz3jxhkhrr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00386",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7206164518",
  "pdf_url": "https://arxiv.org/pdf/2609.00386",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f03rz3jxhkhrr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00386",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00386"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Almost $k$-th powers in short intervals",
  "title_text": "Almost k-th powers in short intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/f03rz3jxhkhrr",
  "venue": "arXiv",
  "versions": []
}