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arXiv · 2501.16766

Quantitative strong approximation for quaternary quadratic forms

Zhizhong Huang·Damaris Schindler·Alec Shute
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Abstract

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.

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Zhizhong Huang, Damaris Schindler, Alec Shute. 2025-01-28. Quantitative strong approximation for quaternary quadratic forms. https://arxiv.org/abs/2501.16766

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