A Generalization of Gauss-Kuzmin-L\'evy Theorem

TL;DR

This paper extends the Gauss-Kuzmin-Lévy theorem to a broader class of transformations called p-numerated generalized Gauss transformations, providing new theoretical insights and estimates for related constants.

Contribution

It introduces a generalized version of the Gauss-Kuzmin-Lévy theorem for p-numerated transformations and estimates the associated constant.

Findings

Proved a generalized Gauss-Kuzmin-Lévy theorem for T_p(x)

Provided an estimate for the constant in the theorem

Extended classical results to a broader class of transformations

Abstract

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.