4 papers · 1 filter
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 , we study the restricted Lagrange spectrum arising from th…
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 . For an integer matrix $M…
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 such that $\left|x-\frac{p}{q}\ri…
On the geometry of the second Lagrange spectra
Hao Cheng, Harold Erazo, Carlos Gustavo Moreira +1
The Lagrange spectrum is the set of finite values of the best approximation constants , where $α\in \mathbb{R}\setminus \mathbb{…