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

Published:2005-04-01
Printed: Apr 2005
• Angel V. Kumchev
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## Abstract

We investigate exceptional sets in the Waring--Goldbach problem. For example, in the cubic case, we show that all but $O(N^{79/84+\epsilon})$ integers subject to the necessary local conditions can be represented as the sum of five cubes of primes. Furthermore, we develop a new device that leads easily to similar estimates for exceptional sets for sums of fourth and higher powers of primes.
 MSC Classifications: 11P32 - Goldbach-type theorems; other additive questions involving primes 11L15 - Weyl sums 11L20 - Sums over primes 11N36 - Applications of sieve methods 11P55 - Applications of the Hardy-Littlewood method [See also 11D85]