{
  "abstract": "As applications of non-standard analysis to the study of transcendence in the ring $\\mathscr{A}$ of integers modulo infinitely large primes, we extend transcendence criteria by Anzawa--Funakura and Matsusaka--Seki. Using the extension of the criterion by Anzawa--Funakura, we observe conditional relation between asymptotic behaviour of prime gaps and transcendence in $\\mathscr{A}$. We also summarise known algebraic and model theoretic results on $\\mathscr{A}$ for number theorists, and share topics in transcendental number theory with algebraists and model theorists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00512",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomoki Mihara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dznmkdzh7k9vt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00512",
  "fulltext_url": null,
  "id": "dznmkdzh7k9vt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00512",
  "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.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical and Theoretical Analysis"
    ]
  ],
  "openalex": "W7160110735",
  "pdf_url": "https://arxiv.org/pdf/2605.00512",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dznmkdzh7k9vt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.00512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes",
  "title_text": "Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/dznmkdzh7k9vt",
  "venue": "arXiv",
  "versions": []
}