Quantitative strong approximation for ternary quadratic forms I
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912143810494464 |
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| author | Huang, Zhizhong |
| author_facet | Huang, Zhizhong |
| contents | We derive asymptotic formulas with a secondary term for the (smoothly weighted) count of number of integer solutions of height $\leqslant B$ with local conditions to the equation $F(x_1,x_2,x_3)=m$, where $F$ is a non-degenerate indefinite ternary integral quadratic form, and $m$ is a non-zero integer satisfying $-mΔ_F=\square$ which can grow like $O(B^{2-θ})$ for some fixed $θ>0$. Our approach is based on the $δ$-variant of the Hardy--Littlewood circle method developed by Heath-Brown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative strong approximation for ternary quadratic forms I Huang, Zhizhong Number Theory 11D45 We derive asymptotic formulas with a secondary term for the (smoothly weighted) count of number of integer solutions of height $\leqslant B$ with local conditions to the equation $F(x_1,x_2,x_3)=m$, where $F$ is a non-degenerate indefinite ternary integral quadratic form, and $m$ is a non-zero integer satisfying $-mΔ_F=\square$ which can grow like $O(B^{2-θ})$ for some fixed $θ>0$. Our approach is based on the $δ$-variant of the Hardy--Littlewood circle method developed by Heath-Brown. |
| title | Quantitative strong approximation for ternary quadratic forms I |
| topic | Number Theory 11D45 |
| url | https://arxiv.org/abs/2412.03350 |