{
  "abstract": "We construct a function $Φ$ such that the orbit under the representation of PSL(2,Z) is an orthonormal basis for the Bergman space with weight $α=12$. Moreover, we show that $Φ$ is effectively computable as a holomorphic function on the upper half-plane (in the precise sense of computable analysis), by providing an effective procedure. This constructs a wandering and tracelike vector for PSL(2,Z), whose abstract existence was proved by Sir Vaughan Jones in his last paper, where the corresponding construction was left as a problem. The function is built using an orthonormalization and modularization method, and it displays modular reminiscencies, despite not being modular itself. provides a computable implementing vector for the abstract anti-isomorphism between the von Neumann algebra $M_{12}(Γ)$ and its commutant, which is generated, in Rădulescu's sense, by cusp-form Toeplitz operators, while Voiculescu's results provide a random matrix model for $M_{12}(Γ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30014",
  "author_total": 1,
  "authors": [
    {
      "name": "Luís Daniel Abreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7heny8fwwpark.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30014",
  "fulltext_url": null,
  "id": "7heny8fwwpark",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30014",
  "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.CV"
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      "arxiv",
      "math.FA"
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      "arxiv",
      "math.NT"
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    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
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  "openalex": "W7214330942",
  "pdf_url": "https://arxiv.org/pdf/2609.30014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7heny8fwwpark.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A computable wandering and tracelike vector for modular orbits in the Bergman space",
  "title_text": "A computable wandering and tracelike vector for modular orbits in the Bergman space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7heny8fwwpark",
  "venue": "arXiv",
  "versions": []
}