Effective Vinogradov's mean value theorem via efficient boxing

TL;DR

This paper improves bounds in Vinogradov's mean value theorem by combining Wooley's efficient congruencing with classical methods, leading to more effective results in analytic number theory.

Contribution

It introduces a novel combination of efficient congruencing with classical techniques to obtain effective bounds in Vinogradov's mean value theorem.

Findings

Derived improved bounds for Vinogradov's mean value theorem.

Demonstrated the effectiveness of combining modern and classical methods.

Provided a framework for future research in exponential sum estimates.

Abstract

We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.