{
  "abstract": "We prove a finiteness theorem for Dirichlet series satisfying the Euler product, analytic continuation, and functional equation expected of a holomorphic newform. For any fixed level $N$, even weight $k$, and exponent $σ$, only finitely many such series have Dirichlet coefficients $\\ll n^σ$. No hypotheses on twists by Dirichlet characters are assumed. The proof combines a combinatorial spanning theorem for Ramanujan sums with an operator-theoretic argument that uses two distinct primes to establish discreteness of the possible Hecke eigenvalues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07921",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew R. Booker"
    },
    {
      "name": "Min Lee"
    },
    {
      "name": "Nina Zubrilina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46n2vncyswznh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07921",
  "fulltext_url": null,
  "id": "46n2vncyswznh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07921",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46n2vncyswznh.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Towards a twistless converse theorem",
  "title_text": "Towards a twistless converse theorem",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/46n2vncyswznh",
  "venue": "arXiv",
  "versions": []
}