Mean value estimates for Weyl sums in two dimensions
Jean Bourgain, Ciprian Demeter
TL;DR
This paper employs decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions, advancing understanding of these exponential sum problems.
Contribution
It introduces new mean value estimates for Weyl sums in two dimensions using decoupling theory, providing novel bounds for quadratic and cubic systems.
Findings
Derived new bounds for Weyl sums in two dimensions
Estimated solutions count for quadratic and cubic Parsell--Vinogradov systems
Enhanced understanding of decoupling applications in exponential sum problems
Abstract
We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.
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