On a Waring-Goldbach type problem for fourth powers

On the Waring-Goldbach problem for eighth and higher powers

Linnik ’ s approximation to Goldbach ’ s conjecture , and other problems

We examine the problem of writing every sufficiently large even number as the sum of two primes and at most K powers of 2. We outline an approach that only just falls short of improving the current bounds on K. Finally, we improve the estimates in other Waring–Goldbach problems.

On Sums of Powers of Almost Equal Primes

We investigate the Waring-Goldbach problem of representing a positive integer n as the sum of s kth powers of almost equal prime numbers. Define sk = 2k(k − 1) when k > 3, and put s2 = 6. In addition, put θ2 = 19 24 , θ3 = 4 5 and θk = 5 6 (k > 4). Suppose that n satisfies the necessary congruence conditions, and put X = (n/s). We show that whenever s > sk and ε > 0, and n is sufficiently large...

A remark on a theorem of the Goldbach - Waring type

On the Waring–goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers

(1.1) p1 + · · ·+ ps = n, where p1, . . . , ps are prime unknowns. It is conjectured that for any pair of integers k, s ∈ N with s ≥ k + 1 there exist a fixed modulus qk,s and a collection Nk,s of congruence classes mod qk,s such that (1.1) is solvable for all sufficiently large n ∈ Nk,s. While a proof of this conjecture appears to be beyond the reach of present methods, some significant progre...