Subconvexity in the inhomogeneous cubic Vinogradov system

When h is an element of Z(3), denote by B(X; h) the number of integral solutions to the system(6) n-expressionry sumexpressiontion ( i=1) (x(i)(j) - y(i)(j)) = h(j) (1 <= j <= 3),with 1 <= x(i), y(i) <= X (1 <= i <= 6). When h(1) &NOTEQUexpressionL; 0 and appropriate local solubility conditions on h are met, we obtain an asymptotic formula for B(X; h), thereby establishing a subconvex local-global principle in the inhomogeneous cubic Vinogradov system. We obtain similar conclusions also when h(1) = 0, h(2) &NOTEQUexpressionL; 0 and X is sufficiently large in terms of h(2). Our arguments involve minor arc estimates going beyond square-root cancellation.