Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 10 min ago
PreprintCC BY 4.0arXiv

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

  • Martin Lind
Open at sourcePDFDOICite

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.

Related

  1. Currently, there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
    David W. Farmer
    Bulletin of the American Mathematical SocietyPeer-reviewedLicence not stated7 citedAlgebra & number theoryOpenAlex
  2. More than 8/9 zeros of the Riemann zeta function are simple or on the critical line
    Cristian Cobeli, Alexandru Zaharescu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Ramanujan Conjecture and Riemann Hypothesis for the unitary groups over function fields
    Luis Alberto Lomelí
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. An Omega result for partial sums of the Riemann zeta function
    Qiyu Yang, Shengbo Zhao
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. On the value distribution of the Riemann zeta-function with general shifts
    Keita Nakai
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{lind2026pvariation,
  title = {{On the $p$-variation of Riemann's "nondifferentiable'' function}},
  author = {Martin Lind},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.21146},
  eprint = {2608.21146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.21146},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the p-variation of Riemann's "nondifferentiable'' function
AU  - Martin Lind
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.21146
UR  - https://arxiv.org/abs/2608.21146
AB  - 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.
ER  -