Multifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915993338511360 |
|---|---|
| author | Alvarado, Matias Arévalo-Hurtado, Nicolás |
| author_facet | Alvarado, Matias Arévalo-Hurtado, Nicolás |
| contents | We study the asymptotic power means of the coefficients associated with the Schneider continued fraction map on $p\mathbb{Z}_p$. Using tools from thermodynamic formalism, we compute the Hausdorff dimension of the corresponding level sets and obtain explicit formulas for the associated multifractal spectra. The locally constant nature of the geometric potential enables a precise description in terms of polylogarithm functions, in sharp contrast with the classical real setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$ Alvarado, Matias Arévalo-Hurtado, Nicolás Dynamical Systems Number Theory We study the asymptotic power means of the coefficients associated with the Schneider continued fraction map on $p\mathbb{Z}_p$. Using tools from thermodynamic formalism, we compute the Hausdorff dimension of the corresponding level sets and obtain explicit formulas for the associated multifractal spectra. The locally constant nature of the geometric potential enables a precise description in terms of polylogarithm functions, in sharp contrast with the classical real setting. |
| title | Multifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$ |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2605.05484 |