Vinogradov's three primes theorem in the intersection of multiple Piatetski-Shapiro sets

TL;DR

This paper extends Vinogradov's three primes theorem to primes constrained within the intersection of multiple Piatetski-Shapiro sequences, demonstrating the theorem's robustness under these additional conditions.

Contribution

It proves that Vinogradov's three primes theorem remains valid when prime variables are restricted to the intersection of multiple Piatetski-Shapiro sequences.

Findings

Vinogradov's theorem holds in this new setting

Prime representations are possible within intersected Piatetski-Shapiro sets

The result broadens understanding of primes in special sequences

Abstract

Vinogradov's three primes theorem indicates that, for every sufficiently large odd integer $N$, the equation $N=p_1+p_2+p_3$ is solvable in prime variables $p_1,p_2,p_3$. 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.