{
  "abstract": "In this paper, we construct new families of imaginary and real quadratic fields that are $p$-rational. In the imaginary case, we prove that for any positive integer $k$ and any integer $m$, the imaginary quadratic field $\\mathbb{Q}\\left(\\sqrt{-(kp+m)}\\right)$ is $p$-rational for sufficiently large primes $p$. The proof relies on Louboutin's bound on the class numbers of imaginary quadratic fields. As a corollary, we recover the $p$-rationality of consecutive quadratic fields, a result due to Chattopadhyay, Laxmi and Saikia \\cite{CLS}. In the real case, we give an explicit proof of the $p$-rationality of the real quadratic field $\\mathbb{Q}\\left(\\sqrt{p(p+1)}\\right)$ for any odd prime $p$, and obtain new pairs of real quadratic fields $\\left(\\mathbb{Q}\\left(\\sqrt{p(p-2)}\\right),\\mathbb{Q}\\left(\\sqrt{p(p-1)}\\right)\\right)$ and $\\left(\\mathbb{Q}\\left(\\sqrt{p(p+1)}\\right),\\mathbb{Q}\\left(\\sqrt{p(p+2)}\\right)\\right)$ for any prime $p>3$. We also construct new examples of $p$-rational triquadratic fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21250",
  "author_total": 2,
  "authors": [
    {
      "name": "Chen Lin"
    },
    {
      "name": "Xuejun Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6590yjh01zrn6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21250",
  "fulltext_url": null,
  "id": "6590yjh01zrn6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21250",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7170880170",
  "pdf_url": "https://arxiv.org/pdf/2607.21250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6590yjh01zrn6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.21250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The $p$-rationality of $\\mathbb{Q}\\left(\\sqrt{-(kp+m)}\\right)$ and $\\mathbb{Q}\\left(\\sqrt{p(p+1)}\\right)$",
  "title_text": "The p-rationality of ℚ(√(−(kp+m))) and ℚ(√(p(p+1)))",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/6590yjh01zrn6",
  "venue": "arXiv",
  "versions": []
}