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On the Waring--Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers |
Canad. J. Math. 57(2005), 298-327
Published:2005-04-01
Printed: Apr 2005
Printed: Apr 2005
- Angel V. Kumchev
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] |