{
  "abstract": "We study the algebraic independence of special values of power series $f(β^{-1})$, where $β$ is a fixed Pisot or Salem number. In particular, we consider the case where $f(X)=\\sum_{n\\geq 0} t(n) X^{w(n)}$ is not a lacunary series and is not assumed to satisfy any special functional equation, such as a Mahler-type functional equation. In our main results, we give a new criterion of the algebraic independence of three values. Applying our main results, we prove that the following three values are algebraically independent: \\[ % \\begin{gathered} \\sum_{n=3}^{\\infty}\\lfloor n^{y}\\rfloorβ^{-\\lfloor n^{\\log \\log n}\\rfloor},\\quad \\sum_{n=3}^{\\infty}β^{-\\lfloor n^{\\log \\log n}\\rfloor},\\quad \\sum_{n=1}^{\\infty}β^{-\\lfloor n^{\\log n}\\rfloor}, % \\end{gathered} \\] where $y$ is an arbitrary positive real number. Since our criterion is flexible, we have considerable freedom in choosing the coefficients $(t(n))_{n\\geq 0}$ and the exponents $(w(n))_{n\\geq 0}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15590",
  "author_total": 3,
  "authors": [
    {
      "name": "Hajime Kaneko"
    },
    {
      "name": "Satoru Oshima"
    },
    {
      "name": "Takafumi Tsurumaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8632beyfgaksq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15590",
  "fulltext_url": null,
  "id": "8632beyfgaksq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15590",
  "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|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7213279735",
  "pdf_url": "https://arxiv.org/pdf/2609.15590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8632beyfgaksq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15590"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An extension of algebraic independence of special values for non-lacunary power series",
  "title_text": "An extension of algebraic independence of special values for non-lacunary power series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8632beyfgaksq",
  "venue": "arXiv",
  "versions": []
}