On the Markoff spectrum on the Hecke group of index six

Byungchul Cha; Dong Han Kim; Deokwon Sim

doi:10.1016/j.indag.2026.01.004

On the Markoff spectrum on the Hecke group of index six

Byungchul Cha
, Dong Han Kim
, Deokwon Sim

Department of Mathematics Education

Hongik University
Samsung

Research output: Contribution to journal › Article › peer-review

Abstract

The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A. Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest accumulation point 4/3. We show that both the Markoff and Lagrange spectra below 4/3+ϵ have positive Hausdorff dimension for any positive ϵ. We also find maximal gaps and an isolated point in the spectra.

Original language	English
Journal	Indagationes Mathematicae
DOIs	https://doi.org/10.1016/j.indag.2026.01.004
State	Accepted/In press - 2026

Keywords

Hecke group
Lagrange spectrum
Markoff spectrum

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10.1016/j.indag.2026.01.004

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title = "On the Markoff spectrum on the Hecke group of index six",

abstract = "The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A. Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest accumulation point 4/3. We show that both the Markoff and Lagrange spectra below 4/3+ϵ have positive Hausdorff dimension for any positive ϵ. We also find maximal gaps and an isolated point in the spectra.",

keywords = "Hecke group, Lagrange spectrum, Markoff spectrum",

author = "Byungchul Cha and Kim, \{Dong Han\} and Deokwon Sim",

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doi = "10.1016/j.indag.2026.01.004",

language = "English",

journal = "Indagationes Mathematicae",

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T1 - On the Markoff spectrum on the Hecke group of index six

AU - Cha, Byungchul

AU - Kim, Dong Han

AU - Sim, Deokwon

PY - 2026

Y1 - 2026

N2 - The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A. Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest accumulation point 4/3. We show that both the Markoff and Lagrange spectra below 4/3+ϵ have positive Hausdorff dimension for any positive ϵ. We also find maximal gaps and an isolated point in the spectra.

AB - The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A. Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest accumulation point 4/3. We show that both the Markoff and Lagrange spectra below 4/3+ϵ have positive Hausdorff dimension for any positive ϵ. We also find maximal gaps and an isolated point in the spectra.

KW - Hecke group

KW - Lagrange spectrum

KW - Markoff spectrum

UR - https://www.scopus.com/pages/publications/105029733701

U2 - 10.1016/j.indag.2026.01.004

DO - 10.1016/j.indag.2026.01.004

M3 - Article

AN - SCOPUS:105029733701

SN - 0019-3577

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

ER -

On the Markoff spectrum on the Hecke group of index six

Abstract

Keywords

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