Multifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$

TL;DR

This paper analyzes the multifractal spectra of power means related to the Schneider map on p-adic integers, using thermodynamic formalism to derive explicit formulas and Hausdorff dimensions.

Contribution

It introduces a p-adic multifractal analysis of the Schneider map, providing explicit formulas and a detailed geometric description.

Findings

Computed Hausdorff dimensions of level sets.

Derived explicit formulas for multifractal spectra.

Revealed contrast with classical real setting through polylogarithm functions.

Abstract

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.