Gerardo González Robert

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math.NT2023

Complex numbers with a prescribed order of approximation and Zaremba's conjecture

Gerardo González Robert, Mumtaz Hussain, Nikita Shulga

Given $b = - A \pm i$ with $A$ being a positive integer, we can represent any complex number as a power series in $b$ with coefficients in $A = {0, 1, \dots, A^{2}}$ . 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 $x \in (0, 1]$ 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{…