Quantitative strong approximation for ternary quadratic forms II

Zhizhong Huang

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arXiv · 2412.05903

Quantitative strong approximation for ternary quadratic forms II

Zhizhong Huang

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Abstract

Let $F$ be a non-degenerate integral ternary quadratic form and let $m_0\in\mathbb{Z}_{\neq 0}$. We study growth of rational points on the affine quadric $(F=m_0)$ and show that they are equidistributed in the adelic space off a finite place. This is closely related to Linnik's problem. Our approach is based on the $\delta$-variant of the Hardy--Littlewood circle method developed by Heath-Brown.

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Zhizhong Huang. 2024-12-08. Quantitative strong approximation for ternary quadratic forms II. https://arxiv.org/abs/2412.05903

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