{
  "abstract": "FINDING: Murmurations in arithmetic L-functions reveal unexpected statistical correlations between elliptic curve coefficients and modular form data, tied to conductor 24 families. | MATH: The murmuration phenomenon involves averaging Fourier coefficients \\(a_p(E)\\) of elliptic curves over families, revealing oscillatory patterns in the distribution of \\(a_p\\) as a function of conductor \\(N\\). Key objects: \\(L(E,s) = \\sum_{n\\ge1} a_n n^{-s}\\), conductor \\(N\\) (with \\(N=24\\) as a notable small case), and the modular form correspondence \\(f_E(q) = \\sum a_n q^n\\). The observed murmurations are statistical — not exact equalities — but show coherent phase alignment in coefficient averages across thousands of curves, suggesting hidden structure in the Sato–Tate distribution beyond the predicted \\( \\sin^2\\theta \\) law. | CONNECTION: Conductor 24 factors as \\(24 = 2^3 \\cdot 3\\), and the associated elliptic curves have complex multiplication or CM-like structure in some cases. The number 24 app\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/8njkwnbzvejxr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635506",
  "fulltext_url": null,
  "id": "8njkwnbzvejxr",
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  "landing_url": "https://zenodo.org/records/23635506",
  "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": [],
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  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8njkwnbzvejxr.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635506",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635506"
    }
  ],
  "subjects": [],
  "title": "Murmurations in L-Functions: Statistical Correlations in Elliptic Curves of Conductor 24 — E8 Intelligence Research",
  "title_text": "Murmurations in L-Functions: Statistical Correlations in Elliptic Curves of Conductor 24 — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/8njkwnbzvejxr",
  "venue": "Zenodo",
  "versions": []
}