Quantitative strong approximation for ternary quadratic forms II

Abstract

Let $F$ be a non-degenerate integral ternary quadratic form and let $m_0\in {\mathbb{Z}}_{\ne 0}$. 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.