A fundamental challenge within the metric theory of continued fractions involves quantifying
sets of real numbers especially when their partial quotients exhibit specific growth rates. For …

We present a detailed Hausdorff dimension analysis of the set of real numbers where the
product of consecutive partial quotients in their continued fraction expansion grow at a …

In this paper, we investigate the dynamics of continued fractions and explore the ergodic
behaviour of the products of mixed partial quotients. For any $ d\geq 1$ and $\Phi:\N\to\R_+ …

For a decreasing real valued function ψ, a pair (A, b) of a real m× n matrix A and b∈ R m is
said to be ψ-Dirichlet improvable if the system‖ A q+ b− p‖ m< ψ (T) and‖ q‖ n< T has a …

The study of products of consecutive partial quotients in the continued fraction arises
naturally out of the improvements to Dirichlet's theorem. We study the distribution of the two …

Abstract Let [a 1 (x), a 2 (x),..., an (x),...] be the continued fraction expansion of an irrational
number x∈(0, 1). The study of the growth rate of the product of consecutive partial quotients …

We prove that the points of Dirichlet spectrum D|·| 2 D^2_|⋅| for two‐dimensional
simultaneous approximation with respect to Euclidean norm can be attained by numbers …

The theory of uniform approximation of real numbers motivates the study of products of
consecutive partial quotients in regular continued fractions. For any non-decreasing positive …

Motivated by recent developments in the metrical theory of continued fractions for real
numbers concerning the growth of consecutive partial quotients, we consider its analogue …

Let be the continued fraction expansion of a real number. The growth properties of the
products of consecutive partial quotients are tied up with the set admitting improvements to …