Integral Hasse principle for Markoff type cubic surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916355701211136 |
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| author | Mishra, Hrishabh |
| author_facet | Mishra, Hrishabh |
| contents | We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x^2+ y^2+ z^2- xyz= a$ with $|a|\leq A$ as $A\to \infty$. Our bound improves upon existing work of Ghosh and Sarnak. As a result, we demonstrate that the integral Hasse principle holds for a density $1$ of surfaces in certain sparse sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral Hasse principle for Markoff type cubic surfaces Mishra, Hrishabh Number Theory 11D85 (11D25, 11D45, 11N32, 11P55) We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x^2+ y^2+ z^2- xyz= a$ with $|a|\leq A$ as $A\to \infty$. Our bound improves upon existing work of Ghosh and Sarnak. As a result, we demonstrate that the integral Hasse principle holds for a density $1$ of surfaces in certain sparse sequences. |
| title | Integral Hasse principle for Markoff type cubic surfaces |
| topic | Number Theory 11D85 (11D25, 11D45, 11N32, 11P55) |
| url | https://arxiv.org/abs/2408.06846 |