{
  "abstract": "We estimate the number of integers up to $x$ whose $y$-friable component exceeds $z$. Uniformly for $\\max\\{2,\\log z\\}\\leqslant y\\leqslant z\\leqslant x/2$, we determine the logarithm of this counting function up to an error $O(\\log z/\\log y)$. This sharpens an estimate arising from a problem in Ford's sieve methods lecture notes. The proof combines classical friable-number estimates with an elementary argument for the lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37507",
  "author_total": 2,
  "authors": [
    {
      "name": "Gérald Tenenbaum"
    },
    {
      "name": "Xiangyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6775rqahe6f4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37507",
  "fulltext_url": null,
  "id": "6775rqahe6f4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37507",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214893876",
  "pdf_url": "https://arxiv.org/pdf/2609.37507",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6775rqahe6f4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.37507",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37507"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On integers whose friable component is large",
  "title_text": "On integers whose friable component is large",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6775rqahe6f4t",
  "venue": "arXiv",
  "versions": []
}