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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16766 |
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| _version_ | 1866916586521100288 |
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| author | Huang, Zhizhong Schindler, Damaris Shute, Alec |
| author_facet | Huang, Zhizhong Schindler, Damaris Shute, Alec |
| contents | The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real place. On the other hand, we also study the growth of integral points on the three-dimensional punctured affine cone, as a quantitative version of strong approximation with Brauer--Manin obstruction for this quasi-affine variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative strong approximation for quaternary quadratic forms Huang, Zhizhong Schindler, Damaris Shute, Alec Number Theory The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real place. On the other hand, we also study the growth of integral points on the three-dimensional punctured affine cone, as a quantitative version of strong approximation with Brauer--Manin obstruction for this quasi-affine variety. |
| title | Quantitative strong approximation for quaternary quadratic forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.16766 |