{
  "abstract": "We investigate the variational properties of Riemann's ''nondifferentiable'' function $R$. We show that $R$ has finite $p$-variation for $p>4/3$ and infinite $p$-variation for $p<4/3$. As an application of our results, we provide a new look on an upper estimate of the Hausdorff dimension of the image of $R$, due to Eceizabarrena.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21146",
  "author_total": 1,
  "authors": [
    {
      "name": "Martin Lind"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7rrnmawawad5v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21146",
  "fulltext_url": null,
  "id": "7rrnmawawad5v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21146",
  "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.CA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7204126929",
  "pdf_url": "https://arxiv.org/pdf/2608.21146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7rrnmawawad5v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.21146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the $p$-variation of Riemann's \"nondifferentiable'' function",
  "title_text": "On the p-variation of Riemann's \"nondifferentiable'' function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/7rrnmawawad5v",
  "venue": "arXiv",
  "versions": []
}