{
  "abstract": "We study explicit denominator conditions ensuring the irrationality of the dilogarithm at positive and negative rational points. We prove that $\\operatorname{Li}_2(p/q)$ is irrational whenever $q>(4e^4/27)p^3$, and obtain an explicit, slightly smaller threshold for $\\operatorname{Li}_2(-p/q)$. The positive argument specializes the Rhin--Viola integral family and uses a uniform estimate for a restricted prime divisor. The negative argument combines the same arithmetic construction with three adjacent integral moments and an explicit maximization. We also give finite-numerator refinements by interpolating certified partition bounds and by introducing a comparison measure with a quadratic tail. In particular, $\\operatorname{Li}_2(5/q)$ is irrational for every integer $q\\ge418$. The proof separates the established integral and determinant constructions from the parameter estimates and finite certificates used here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01066",
  "author_total": 2,
  "authors": [
    {
      "name": "Hu Tan"
    },
    {
      "name": "Ying Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3048xrtqbnth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01066",
  "fulltext_url": null,
  "id": "d3048xrtqbnth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01066",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3048xrtqbnth.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01066"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Uniform cubic bounds for irrational values of the dilogarithm",
  "title_text": "Uniform cubic bounds for irrational values of the dilogarithm",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d3048xrtqbnth",
  "venue": "arXiv",
  "versions": []
}