Vinogradov’s three primes theorem in the intersection of multiple Piatetski–Shapiro sets

Vinogradov’s three primes theorem indicates that, for every sufficiently large odd integer N, the equation \(N=p_1+p_2+p_3\) $N=p_1+p_2+p_3$ is solvable in prime variables \(p_1,p_2,p_3\) $p_1,p_2,p_3$ . In this paper, it is proved that Vinogradov’s three primes theorem still holds with three prime variables constrained in the intersection of multiple Piatetski–Shapiro sequences.