On the Markoff spectrum on the Hecke group of index six

Byungchul Cha; Dong Han Kim; Deokwon Sim

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arXiv · 2506.08358

On the Markoff spectrum on the Hecke group of index six

Byungchul Cha·Dong Han Kim·Deokwon Sim

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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 $4/\sqrt3$. We show that both the Markoff and Lagrange spectra below $4/\sqrt{3} + \epsilon$ have positive Hausdorff dimension for any positive $\epsilon$. We also find maximal gaps and an isolated point in the spectra.

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Byungchul Cha, Dong Han Kim, Deokwon Sim. 2025-06-10. On the Markoff spectrum on the Hecke group of index six. https://arxiv.org/abs/2506.08358

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