On integer solutions of Parsell-Vinogradov systems

TL;DR

This paper establishes a precise upper bound on the count of integer solutions to the Parsell-Vinogradov system across all dimensions starting from two, advancing understanding of these polynomial systems.

Contribution

It provides a sharp, dimension-independent upper bound on solutions, improving previous estimates and deepening theoretical insights into the Parsell-Vinogradov systems.

Findings

Proved a sharp upper bound valid in all dimensions $d \,\geq\ 2$.

Enhanced understanding of the distribution of solutions to polynomial systems.

Advanced the theoretical framework for analyzing polynomial solution counts.

Abstract

We prove a sharp upper bound on the number of integer solutions of the Parsell-Vinogradov system in every dimension $d\ge 2$.