{
  "abstract": "We study rational approximation to logarithms of positive rational numbers and give a separated-weight determinant argument for $μ(\\log r)=2$ whenever $r\\in\\mathbb Q_{>0}\\setminus\\{1\\}$. The geometric input is an interpolation theorem for logarithmic jets at points with distinct multiplicative coordinates. Its successive weight thresholds are independent of the interpolation centres; the eventual degree threshold may depend on them. A local intersection-length bound and a curve inequality lead to surjectivity through a blow-up and Serre vanishing. For a fixed rational argument, this produces a nonzero rational determinant. Clearing denominators gives an arithmetic lower bound, while an exact row translation and repeated Taylor indices yield a contradictory analytic upper bound. The consequences include nonzero rational linear combinations of such logarithms, rational affine changes, and logarithms of positive numbers with a rational positive integer power. We also give a bounded-fibre interpolation extension, an explicit bound for the final analytic degree, and a counterexample to interpolation under the volume condition alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10192",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingwen Liu"
    },
    {
      "name": "Kai Jiang"
    },
    {
      "name": "Pingwen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00e44rb3e5mc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10192",
  "fulltext_url": null,
  "id": "00e44rb3e5mc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10192",
  "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": "W7220991765",
  "pdf_url": "https://arxiv.org/pdf/2610.10192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00e44rb3e5mc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Irrationality exponents of logarithms of positive rational numbers",
  "title_text": "Irrationality exponents of logarithms of positive rational numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/00e44rb3e5mc6",
  "venue": "arXiv",
  "versions": []
}