论文标题
代数品种的有效局部全球原理和有限领域的总产品问题
An effective local-global principle for algebraic varieties and the sum product problem in finite fields
论文作者
论文摘要
我们使用有关$ \ mathbb {c} $上代数品种上的零数的最新结果，该零是由多项式定义的，由多项式具有整数系数，并在其降低模量上足够大的素数，可以研究与线性形式的产品和互惠的质量。这使我们能够在B. Murphy，G。Petridis，O。Roche-Newton，M。Rudnev和I. D. Shkredov（2019）中取得一些进展。
We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, defined by polynomials with integer coefficients, and on their reductions modulo sufficiently large primes to study congruences with products and reciprocals of linear forms. This allows us to make some progress towards a question of B. Murphy, G. Petridis, O. Roche-Newton, M. Rudnev and I. D. Shkredov (2019) on an extreme case of the Erdős-Szemerédi conjecture in finite fields.
