A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem

Abstract

We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely does solution counting in older partial progress on Vinogradov's mean value theorem correspond to in Fourier decoupling theory.

25 pages; revised version incorporating referee comments, to appear in Mathematika