Proof of the main conjecture in Vinogradov’s Mean Value Theorem for degrees higher than three

Pages 633-682 from Volume 184 (2016), Issue 2 by Jean Bourgain, Ciprian Demeter, Larry Guth

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.

Keywords
, , ,
Mathematical Subject Classification

Primary 2000: ,

DOI
https://doi.org/10.4007/annals.2016.184.2.7
MR
3548534
zbMATH
06662221
Milestones
Received: 14 December 2015
Revised: 18 April 2016
Accepted: 1 February 2016
Published online: 29 July 2016

Authors

Jean Bourgain

School of Mathematics, Institute for Advanced Study, Princeton, NJ

Ciprian Demeter

Department of Mathematics, Indiana University, Bloomington, IN

Larry Guth

Department of Mathematics, MIT, Cambridge, MA