@article{10765,
  abstract     = {We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics.},
  author       = {Cao, Yang and Huang, Zhizhong},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  number       = {3},
  publisher    = {Elsevier},
  title        = {{Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics}},
  doi          = {10.1016/j.aim.2022.108236},
  volume       = {398},
  year         = {2022},
}