Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics

Yang Cao, Zhizhong Huang

We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form $q(x_1,\cdots ,x_n)=m$, where $q$ is a non-degenerate integ…