The ternary Goldbach problem with primes in positive density sets

Quanli Shen

Let $\mathcal{P}$ denote the set of all primes. $P_1,P_2,P_3$ are three subsets of $\mathcal{P}$. Let $\underline{\delta }(P_i)$ $(i=1,2,3)$ denote the lower density of $P_i$ in…