On Waring's Problem VIII

Let G(f) denote the least value of s such that every large integer is the sum of s or fewer values of the polynomial f(x) of degree n. Loo-Keng Hua under certain conditions and the author under milder conditions independently proved certain results which are roughly equivalent to the result

G(f)=O(n³ log n).

In this paper under still milder conditions certain results about G(f) are proved, which are roughly equivalent to Vinogradow's result for G(n). A lemma of Hua (Lemma 12) plays an important part in this paper.