{
  "abstract": "In this paper we explore the concept of smoothness in arithmetic semigroups. In particular, we give explicit asymptotics for the counting function $Ψ_G(x,y)$ when the arithmetic semigroup $G$ satisfies Axiom A (in the spirit of Knopfmacher). The asymptotics generalise the standard results in the literature for the integer case, and are expressed in terms of the Dickman $ρ$ function. Finally, we give applications of our results to counting smooth families of finite abelian groups and finite semisimple rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29748",
  "author_total": 3,
  "authors": [
    {
      "name": "Giovanna De Lauri"
    },
    {
      "name": "Dan Fretwell"
    },
    {
      "name": "Jack Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wbgvgkqa71k5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29748",
  "fulltext_url": null,
  "id": "9wbgvgkqa71k5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29748",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214392556",
  "pdf_url": "https://arxiv.org/pdf/2609.29748",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wbgvgkqa71k5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29748",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29748"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On smooth elements in arithmetic semigroups",
  "title_text": "On smooth elements in arithmetic semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/9wbgvgkqa71k5",
  "venue": "arXiv",
  "versions": []
}