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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16810 |
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| _version_ | 1866929327580381184 |
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| author | Kotsovolis, Giorgos |
| author_facet | Kotsovolis, Giorgos |
| contents | We give a complete list of the points in the spectrum $$\mathcal{Z}=\{\inf_{(x,y)\inΛ,xy\neq0}{\left\vert xy\right\vert},\,\text{$Λ$ is a unimodular rational lattice of $\mathbb{R}^2$}\}$$ above $\frac{1}{3}.$ We further show that the set of limit points of $\mathcal{Z}$ with values larger than $\frac{1}{3},$ is equal to the set $\{\frac{2m}{\sqrt{9m^2-4}+3m},\text{ where $m$ is a Markoff number}\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Spectrum of $\mathbb{Q}$-Isotropic Binary Quadratic Forms Kotsovolis, Giorgos Number Theory Dynamical Systems 11J06, 11H50 We give a complete list of the points in the spectrum $$\mathcal{Z}=\{\inf_{(x,y)\inΛ,xy\neq0}{\left\vert xy\right\vert},\,\text{$Λ$ is a unimodular rational lattice of $\mathbb{R}^2$}\}$$ above $\frac{1}{3}.$ We further show that the set of limit points of $\mathcal{Z}$ with values larger than $\frac{1}{3},$ is equal to the set $\{\frac{2m}{\sqrt{9m^2-4}+3m},\text{ where $m$ is a Markoff number}\}$. |
| title | The Spectrum of $\mathbb{Q}$-Isotropic Binary Quadratic Forms |
| topic | Number Theory Dynamical Systems 11J06, 11H50 |
| url | https://arxiv.org/abs/2404.16810 |