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arXiv · 2003.07287

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

Yang Cao·Zhizhong Huang
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Abstract

We establish the Hardy-Littlewood property (\`a 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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Yang Cao, Zhizhong Huang. 2020-03-16. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. https://arxiv.org/abs/2003.07287

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