On the Markoff spectrum on the Hecke group of index six
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908780221956096 |
|---|---|
| author | Cha, Byungchul Kim, Dong Han Sim, Deokwon |
| author_facet | Cha, Byungchul Kim, Dong Han Sim, Deokwon |
| contents | 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 $4/\sqrt{3} + ε$ have positive Hausdorff dimension for any positive $ε$. We also find maximal gaps and an isolated point in the spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Markoff spectrum on the Hecke group of index six Cha, Byungchul Kim, Dong Han Sim, Deokwon Number Theory Dynamical Systems 11J06, 11J70 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 $4/\sqrt{3} + ε$ have positive Hausdorff dimension for any positive $ε$. We also find maximal gaps and an isolated point in the spectra. |
| title | On the Markoff spectrum on the Hecke group of index six |
| topic | Number Theory Dynamical Systems 11J06, 11J70 |
| url | https://arxiv.org/abs/2506.08358 |