2 papers
math.NT2024
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…
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{…