8 citations · 15 across the 11 of their papers we have counts for
Showing 2023 · math.NTShow all
3 papers · 2 filters
math.NT2023
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…
math.NT2023
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{…
math.NT2023★ 2 cited
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…