On certain statistical properties of continued fractions with even and with odd partial quotients

TL;DR

This paper investigates the statistical properties of continued fractions with even, odd, and Nakada's lpha-expansions, focusing on the joint distribution of renewal times and digits in random irrational numbers.

Contribution

It provides new results on the joint limiting distribution of renewal times and digits for various types of continued fraction expansions.

Findings

Established joint limiting distributions for even and odd partial quotients

Extended results to Nakada's lpha-expansions

Enhanced understanding of statistical properties of continued fractions

Abstract

We prove results concerning the joint limiting distribution of the renewal time of denominators and consecutive digits of random irrational numbers in the case of continued fractions with even partial quotients, with odd partial quotients, and for Nakada's \alpha-expansions.