{
  "abstract": "We introduce a systematic framework for constructing holonomic recurrences from meromorphic modular forms. Its central ingredient is a modular analogue of creative telescoping, which turns finite-dimensional quotients of spaces of meromorphic modular forms into explicit recurrence operators. This provides a common explanation for several previously isolated examples: it recovers Apéry's recurrence, Beukers' modular constructions and Zagier's seven sporadic recurrences. The framework also produces a large collection of new examples across different weights and groups. The modular origin of these sequences also confers them with non-trivial arithmetic properties, such as denominator bounds, irrationality statements, and $p$-adic congruences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17240",
  "author_total": 1,
  "authors": [
    {
      "name": "Kam Cheong Au"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5cj1pws0pdt01.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17240",
  "fulltext_url": null,
  "id": "5cj1pws0pdt01",
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  "landing_url": "https://arxiv.org/abs/2610.17240",
  "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"
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      "openalex",
      "2602|Advanced Mathematical Identities"
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  "openalex": "W7221786509",
  "pdf_url": "https://arxiv.org/pdf/2610.17240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5cj1pws0pdt01.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Holonomic sequences arising from meromorphic modular forms",
  "title_text": "Holonomic sequences arising from meromorphic modular forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5cj1pws0pdt01",
  "venue": "arXiv",
  "versions": []
}