On Sums of Products in \(\mathbb{F}_p \times \mathbb{F}_p\)

Resumo

The problem of sums of products in \(\mathbb{F}_p \times \mathbb{F}_p\) is considered. An estimate for sums of products improving Bourgain’s result of 2005 is obtained. This estimate is applied to the problem of estimating polynomial exponential sums over multiplicative subgroups in \(\mathbb{F}_p^*\).