On the Waring--Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers

[摘要] We investigate exceptional sets in the Waring--Goldbach problem. Forexample, in the cubic case, we show that all but$O(N^{79/84+epsilon})$ integers subject to the necessary localconditions can be represented as the sum of five cubes of primes.Furthermore, we develop a new device that leads easily to similarestimates for exceptional sets for sums of fourth and higher powers ofprimes.

[学科分类] 数学（综合）