Harold S. Erazo

activity

20242026

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math.NT2024

inf(M \ L)=3

Harold Erazo, Davi Lima, Carlos Matheus +2

The Lagrange and Markov spectra $L$ and $M$ describe the best constants of Diophantine approximations for irrational numbers and binary quadratic forms. In 1880, A. Markov showed t…

math.NT2024

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…

math.NT2024

New portions of $M ∖ L$ and a lower bound on the Hausdorff distance between $L$ and $M$

Clément Rieutord, Carlos Gustavo Moreira, Harold Erazo

Let $M$ and $L$ be the Markov and Lagrange spectra, respectively. It is known that $L$ is contained in $M$ and Freiman showed in 1968 that $M ∖ L \neq = \emptyset$ . In 2018 the…

inf(M \ L)=3

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

New portions of M∖L and a lower bound on the Hausdorff distance between L and M

New portions of $M ∖ L$ and a lower bound on the Hausdorff distance between $L$ and $M$