8 citations · 15 across the 11 of their papers we have counts for
12 papers
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…
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…
Restricted slowly growing digits for infinite iterated function systems
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1
For an infinite iterated function system on with an attractor and for an infinite subset , consider the set \[ \mathbb E…
Complex numbers with a prescribed order of approximation and Zaremba's conjecture
Gerardo González Robert, Mumtaz Hussain, Nikita Shulga
Given with being a positive integer, we can represent any complex number as a power series in with coefficients in . We prove th…
Metrical properties of weighted products of consecutive Lüroth digits
Adam Brown-Sarre, Gerardo González Robert, Mumtaz Hussain
The Lüroth expansion of a real number is the series \[ x= \frac{1}{d_1} + \frac{1}{d_1(d_1-1)d_2} + \frac{1}{d_1(d_1-1)d_2(d_2-1)d_3} + \cdots, \] with $d_j\in\mathbb{…
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…
Chaotic sets and Hausdorff dimension for Lüroth expansions
Rafael Alcaraz Barrera, Gerardo González Robert
We provide new similarities between regular continued fractions and Lüroth series in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete a…
A Complex Borel-Bernstein Theorem
Gerardo González Robert
Zero-one laws are a central topic in metric Diophantine approximation. A classical example of such laws is the Borel-Bernstein theorem. In this note, we prove a complex analogue of…
Hausdorff dimension of sets of numbers with large Lüroth elements
Aubin Arroyo, Gerardo González Robert
Lüroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and…
Good's Theorem for Hurwitz Continued Fractions
Gerardo González Robert
Good's Theorem for regular continued fraction states that the set of real numbers such that has Hausdorff dimensi…
Purely Periodic and Transcendental Complex Continued Fractions
Gerardo Gonzalez Robert
Adolf Hurwitz proposed in 1887 a continued fraction algorithm for complex numbers: Hurwitz continued fractions (HCF). Among other similarities between HCF and regular continued fra…
Generalized Thue-Morse Continued Fractions
Gerardo González Robert
The Thue-Morse sequence is generalized to the sequences and two equivalent definitions are given. This generalization leads to transcendental numbers and has Queffélec's the…