论文标题
硬质木材属性的算术纯度和仿射四边形的几何筛子
Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics
论文作者
论文摘要
我们为Zariski开放子集建立了hardy-littlewood（àlaborovoi-rudnick），该子集是$ q（x_1，\ cdots，x_n）= m $的形式的仿制四，其中$ q $是一种非基础的积分式Quadratic Quadratic Quadratic form in $ n \ geqslant 3 $ $ $ able- $ variable and-$ m is a non-iSe and-is a s a a a a a a a a s a a a a。这给出了以副率多项式值的积分点的密度的渐近公式，这是仿射四边形无穷大的算术纯度的算术纯度的定量版本。
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.
