{
  "abstract": "We prove a mean value theorem on the distribution of smooth numbers in two simultaneous arithmetic progressions, with generalizing a result of Drappeau. Let $\\varepsilon>0$ and $(\\log x)^C<y<x^{1/C}$ for a sufficiently large $C$. Our result implies that $y$-smooth numbers are well-distributed in the residue classes of a fixed integer $a$ on average over moduli $\\leq x^{5/9-\\varepsilon}$ for each $|a|\\leq x$, which improves Drappeau's range $\\leq x^{6/11-\\varepsilon}$. As an application, we show that a positive proportion of $y$-smooth numbers $n\\leq x$ satisfy $\\min(P^+(n-1), P^+(n+1))>x^{407/720}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01522",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiyuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42vnpz0dc970e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01522",
  "fulltext_url": null,
  "id": "42vnpz0dc970e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01522",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42vnpz0dc970e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01522"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Smooth numbers in simultaneous arithmetic progressions",
  "title_text": "Smooth numbers in simultaneous arithmetic progressions",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/42vnpz0dc970e",
  "venue": "arXiv",
  "versions": []
}