论文标题
Hecke Group H4上的Markoff和Lagrange光谱
The Markoff and Lagrange spectra on the Hecke group H4
论文作者
论文摘要
我们考虑Hecke组$ \ Mathbf H_4 $上的Markoff Spectrum和Lagrange频谱。它们与单位圆的Markoff和Lagrange光谱相同。 $ \ Mathbf H_4 $上的Markoff Spectrum也被称为Vulakh的索引2 Sublattices的Markoff Spectrum和Schmidt的2分钟形式的Markoff Spectrum或$ C $ -Minimal Forms的Markoff Spectrum。他们将频谱描述为第一个积累点。我们表明，在第一个积累点之后，两个光谱都具有正偏度尺寸。然后，我们在光谱中发现了差距，并在Hall的射线上绑定了一个束缚。
We consider the Markoff spectrum and the Lagrange spectrum on the Hecke group $\mathbf H_4$. They are identical with the Markoff and Lagrange spectra of the unit circle. The Markoff spectrum on $\mathbf H_4$ is also 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. They characterized the spectrum up to the first accumulation point, independently. We show that, after the first accumulation point, both spectra have positive Hausdorff dimension. Then we find gaps in the spectra and give a bound on Hall's ray.
