4 papers
Measure theoretic properties of large products of consecutive partial quotients
Adam Brown-Sarre, Gerardo González Robert, Mumtaz Hussain
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…
Approximation by uniformly distributed sequences
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
We consider approximation properties of real points by uniformly distributed sequences. Under some assumptions on the approximation functions, we prove a Khintchine-type - di…
Metrical properties of Hurwitz Continued Fractions
Yann Bugeaud, Gerardo Gonzalez Robert, Mumtaz Hussain
We develop the geometry of Hurwitz continued fractions, a major tool in understanding the approximation properties of complex numbers by ratios of Gaussian integers. Based on a tho…
Transcendence and normality of complex numbers via Hurwitz continued fractions
Felipe GarcÃa-Ramos, Gerardo González Robert, Mumtaz Hussain
We study the topological, dynamical, and descriptive set theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian…