Carlos Gustavo Moreira

collaborators

6 papers

math.NT2026

The ratio spectrum of Lagrange constants under linear fractional transformations

Harold Erazo, Carlos Gustavo Moreira

In this note we solve a problem posed by Lagarias and Shallit concerning Lagrange constants under linear fractional transformations $M x = \frac{a x + b}{c x + d}$ . For an integer matrix $M…

math.NT2026

Generalized Hausdorff dimension of irrationals with Lagrange value exactly 3

Carlos Gustavo Moreira, Harold Erazo, Nicolas Angelini

We study the generalized Hausdorff dimension of some natural subsets of $k^{- 1} (3)$ , where $k^{- 1} (3)$ consists of the real numbers $x$ for which $\left| x-\frac{p}{q} \right|<\fra…

math.NT2026

On very badly approximable numbers

Zhe Cao, Harold Erazo, Carlos Gustavo Moreira

We prove a refined version of Markov's theorem in Diophantine approximation. More precisely, we characterize completely the set of irrationals $x$ such that $\left|x-\frac{p}{q}\ri…

math.NT2026

On the geometry of the second Lagrange spectra

Hao Cheng, Harold Erazo, Carlos Gustavo Moreira +1

The Lagrange spectrum $L$ is the set of finite values of the best approximation constants $k (I^\pm) = lim sup_{∣ p ∣, ∣ q ∣ \to \infty} ∣ q (q I^\pm - p) ∣^{- 1}$ , where $Î±\in \mathbb{R}\setminus \math…

math.NT2026

On irrationals with Lagrange value exactly 3

Zhe Cao, Harold Erazo, Carlos Gustavo Moreira

For $c > 0$ , let $X_{c}$ denote the set of $x \in R \ Q$ such that $x - \frac{p}{q} < \frac{1}{c q ^{2}}$ has only finitely many rational solutions $\frac…

math.NT2025

On the classical Lagrange and Markov spectra: new results on the local dimension and the geometry of the difference set

Harold Erazo, Luke Jeffreys, Carlos Gustavo Moreira

Let $L$ and $M$ denote the classical Lagrange and Markov spectra, respectively. It is known that $L \subset M$ and that $M ∖ L \neq = \emptyset$ . Inspired by three questions as…