{
  "abstract": "Dickman's function $ρ(u)$ denotes the natural density of integers $n$ whose largest prime factor does not exceed $n^{1/u}$. We establish numerically explicit upper and lower bounds for $ρ(u)$, resulting in estimates with a relative error of less than $0.005/u^2$ for all $u\\ge 5$. This allows for an approximate evaluation of $ρ(u)$ without the need to solve the delay differential equation numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.07785",
  "author_total": 1,
  "authors": [
    {
      "name": "Andreas Weingartner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7par3hen19a2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.07785",
  "fulltext_url": null,
  "id": "b7par3hen19a2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.07785",
  "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.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7164049034",
  "pdf_url": "https://arxiv.org/pdf/2606.07785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7par3hen19a2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2606.07785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.07785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Explicit bounds for Dickman's function",
  "title_text": "Explicit bounds for Dickman's function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/b7par3hen19a2",
  "venue": "arXiv",
  "versions": []
}