Work

On the $p$-variation of Riemann's "nondifferentiable'' function

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.21146

Author: Lind, Martin

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204126929

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