Some refinements of error terms estimates for certain additive problems with primes

Abstract

We study, under the assumption of the Generalized Riemann Hypothesis, the individual and mean-square error terms for the number of integers representable as a sum of k≥3 primes. We improve, using a smoothing technique, Friedlander-Goldston's recent results on this topic. Moreover, we remark that the argument we use can also be applied to other similar problems. © 2000 Academic Press.