{
  "abstract": "Let $α>0$ be an irrational number of finite type and let $β\\in\\mathbb{R}$. Assuming the infinitude of Siegel zeros (respectively, sufficiently strong Siegel zeros), we show that for every sufficiently small $\\varepsilon>0$, there exist infinitely many primes $p$ such that \\begin{gather*} \\|αp+β\\|\\leq p^{-1/3+\\varepsilon} \\qquad\\text{(respectively, }\\|αp+β\\|\\leq p^{-1/3-1/20}\\text{)}. \\end{gather*}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30207",
  "author_total": 2,
  "authors": [
    {
      "name": "Sun-Kai Leung"
    },
    {
      "name": "Stelios Sachpazis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyy8tbwtmywgf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30207",
  "fulltext_url": null,
  "id": "eyy8tbwtmywgf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30207",
  "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": "W7214326821",
  "pdf_url": "https://arxiv.org/pdf/2609.30207",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyy8tbwtmywgf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Diophantine approximation by primes and Landau--Siegel zeros",
  "title_text": "Diophantine approximation by primes and Landau--Siegel zeros",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/eyy8tbwtmywgf",
  "venue": "arXiv",
  "versions": []
}