Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics
英文摘要：
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 integral quadratic form in $n\geqslant 3$ 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.
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