On the Markoff spectrum on the Hecke group of index six

초록

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. © 2026 Royal Dutch Mathematical Society (KWG).

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