{
  "abstract": "FINDING: Drinfeld modular forms connect Hecke eigenvalues to q-expansion coefficients over function fields, mirroring classical modular form arithmetic. | MATH: Classical: \\(T_n f = \\lambda_n f\\), \\(f(q)=\\sum a_n q^n\\), \\(a_{mn}=a_m a_n\\) for \\((m,n)=1\\), \\(a_{p^{r+1}}=a_p a_{p^r}-p^{k-1}a_{p^{r-1}}\\). Drinfeld analogue: Hecke operators \\(T_{\\mathfrak p}\\) act on Drinfeld cusp forms; eigenvalues \\(\\lambda_{\\mathfrak p}\\) satisfy \\(a_{\\mathfrak p} = \\lambda_{\\mathfrak p}\\) for good primes, with \\(q\\)-expansion over \\(\\mathbb F_q(T)\\). Armana's work: bounds/relations for coefficients \\(a_n\\) in Drinfeld setting, including \\(a_{n} = \\lambda_{\\mathfrak p} a_{n/\\mathfrak p} - |\\mathfrak p|^{k-1} a_{n/\\mathfrak p^2}\\) for \\(\\mathfrak p | n\\). | CONNECTION: The Hecke algebra is a commutative ring generated by operators indexed by ideals — a lattice/root-system-like structure (the divisor lattice of \\(\\mathbb F_q[T]\\)). Eigenvalues are algebraic integers, and the constant \\(q^{k-1}\\) (where \\(\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52r87dqydkna7.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658203",
  "fulltext_url": null,
  "id": "52r87dqydkna7",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23658203",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52r87dqydkna7.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:38Z",
      "native_id": "23658203",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658203"
    }
  ],
  "subjects": [],
  "title": "Drinfeld Modular Forms Mirror Classical Hecke Eigenvalues and q-Expansion Arithmetic — E8 Intelligence Research",
  "title_text": "Drinfeld Modular Forms Mirror Classical Hecke Eigenvalues and q-Expansion Arithmetic — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:38Z",
  "url": "https://research.draconitic.com/paper/52r87dqydkna7",
  "venue": "Zenodo",
  "versions": []
}