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.