ON THE INHOMOGENEOUS VINOGRADOV SYSTEM

Artikel i vetenskaplig tidskrift, 2022

We show that the system of equations Sigma(s)(i=1)(x(i)(j) - y(i)(j)) = a(j) (1 <= j <= k) has appreciably fewer solutions in the subcritical range s < 1/2k(k + 1) than its homogeneous counterpart, provided that al not equal 0 for some l <= k - 1. Our methods use Vinogradov's mean value theorem in combination with a shifting argument.