The Markoff spectrum on the Hecke group – Dong Han Kim (Dongguk University)

We consider the Markoff spectrum on the Hecke group. The Markoff spectrum on H4 is known as the Markoff spectrum of index 2 sublattices by Vulakh and the Markoff spectrum of 2-minimal forms or C-minimal forms by Schmidt, who characterized the spectrum up to the first accumulation point. The Markoff spectrum on H6 is also known as the Markoff spectrum of 3-minimal forms by Schmidt. After the first accumulation point, we show that both spectra have positive Hausdorff dimension and find gaps. This talk is based on joint work with Byungchul Cha and Deokwon Sim.