M∖L is Not Closed-Reference-Cited by-同舟云学术

M∖L is Not Closed

Published:2020-05-28 Issue:1 Volume:2022 Page:265-311
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Lima Davi¹,Matheus Carlos²,Gustavo Moreira Carlos³⁴,Vieira Sandoel⁴

Affiliation:

1. Instituto de Matemática, UFAL, Av. Lourival Melo Mota s/n, Macei, 57072-900 Alagoas, Brazil

2. CMLS, École Polytechnique, CNRS (UMR 7640), 91128 Palaiseau, France

3. School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China

4. IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil

Abstract

Abstract We show that $1+3/\sqrt{2}$ is a point of the Lagrange spectrum $L$ that is accumulated by a sequence of elements of the complement $M\!\setminus\! L$ of the Lagrange spectrum in the Markov spectrum $M$. In particular, $M\!\setminus\! L$ is not a closed subset of $\mathbb{R}$, so that a question by T. Bousch has a negative answer.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2022/1/265/42136520/rnaa096.pdf

Reference7 articles.

1. Continued fractions and the Markoff tree;Bombieri;Expo. Math.,2007

2. The Markoff and Lagrange spectra;Cusick;Math. Surveys Monogr.,1989

3. Non-coincidence of the spectra of Markov and of Lagrange;Freiman;Mat. Zametki,1968

4. $M\backslash L$ near 3;Lima,2019

5. Markov spectrum near Freiman’s isolated points in $M\backslash L$;Matheus;J. Number Theory,2019

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Lagrange-like spectrum of perfect additive complements;Acta Arithmetica;2024

2. M ∖ L Near 3;Moscow Mathematical Journal;2021