Carlos Gustavo Moreira

activity

20242026

collaborators

9 papers

math.NT2026

Lagrange spectrum for Diophantine approximations of complex numbers with real part equal to one half

Hao Cheng, Harold Erazo, Carlos Gustavo Moreira +1

Motivated by a theorem of A. Schmidt on the part of the complex Lagrange spectrum below $2$ , we study the restricted Lagrange spectrum $L_{\frac{1}{2} + i R}$ arising from th…

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

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 $k (α) = lim sup_{∣ p ∣, ∣ q ∣ \to \infty} ∣ q (q α - p) ∣^{- 1}$ , where $α\in \mathbb{R}\setminus \mathbb{…

math.NT2025

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.NT2025

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…