{
  "abstract": "Let P be the Pascal transformation on the space Omega={0,1}^N, endowed with the Bernoulli measure of parameters (p0,1-p0), where 0 < p0 < 1. A special cohomological equation associated to P is considered, and in particular the following result is proved: exp(2pi it) is an eigenvalue of P if and only if \\sum_{n≥0} DZ(t.C(n,w_0+...+w_{n-1}))^2 < \\infty for almost all (w_0,w_1,...) in Omega, where the C(n,p)=n!/p!(n-p)! are the binomial coefficients and DZ(x) the distance of x to the nearest integer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Thierry Bousch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbs3dpx6rq6br.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "fbs3dpx6rq6br",
  "issns": [],
  "landing_url": "https://hal.science/hal-05830238v1",
  "language": "fr",
  "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": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05830238/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbs3dpx6rq6br.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05830238",
      "source": "hal",
      "url": "https://hal.science/hal-05830238v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "A cohomological equation related to the Pascal transformation",
  "title_text": "A cohomological equation related to the Pascal transformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/fbs3dpx6rq6br",
  "venue": "HAL",
  "versions": []
}