Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three

TL;DR

This paper proves the main conjecture in Vinogradov's Mean Value Theorem for degrees above three by establishing a sharp decoupling inequality for curves, advancing understanding in analytic number theory.

Contribution

It introduces a new sharp decoupling inequality for curves that confirms the main conjecture for higher degrees in Vinogradov's theorem.

Findings

Main conjecture proven for degrees > 3

Decoupling inequality established for curves

Advances in analytic number theory techniques

Abstract

We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This will be a consequence of a sharp decoupling inequality for curves