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

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.

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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