{
  "abstract": "We estimate the number of integers up to x whose y-friable component exceeds z. Uniformly for max{2, log z} ⩽ y ⩽ z ⩽ 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 friablenumber estimates with an elementary argument for the lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Gérald Tenenbaum"
    },
    {
      "name": "Xiangyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ska4pvtmd1ce.bib",
  "cited_by": 0,
  "doi": "10.13140/rg.2.2.13436.50563",
  "fulltext_url": null,
  "id": "6ska4pvtmd1ce",
  "issns": [],
  "landing_url": "https://hal.science/hal-05792809v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-nt"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221758288",
  "pdf_url": "https://hal.science/hal-05792809/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ska4pvtmd1ce.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "hal-05792809",
      "source": "hal",
      "url": "https://hal.science/hal-05792809v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.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": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/6ska4pvtmd1ce",
  "venue": "HAL",
  "versions": []
}