Quantitative strong approximation for ternary quadratic forms III

Abstract

We prove asymptotic formulas for counting (primitive) integral points with local conditions on the (punctured) affine cone defined by a non-singular integral ternary quadratic form, and we relate our results to the Brauer--Manin obstruction. Our approach is based on the $\delta$-variant of the Hardy--Littlewood circle method developed by Heath-Brown.