Hua's Theorem with the Primes in Piatetski-Shapiro Prime Sets

TL;DR

This paper extends Hua's theorem by exploring primes within Piatetski-Shapiro prime sets, specifically addressing the nonhomogeneous case for k=3, thereby advancing classical prime number results.

Contribution

It introduces new results connecting Hua's theorem with Piatetski-Shapiro primes, focusing on the nonhomogeneous case k=3, and deepens the understanding of prime distributions.

Findings

Results in the nonhomogeneous case k=3 for primes in Piatetski-Shapiro sets

Extension of Hua's theorem to hybrid prime problems

Enhanced understanding of prime distribution in specialized sets

Abstract

In this paper, we study the hybrid problem of Hua's theorem and the Piatetski-Shapiro prime number theorem, and obtain results in this direction of the nonhomogeneous case $k=3$, which deepen the classical result of Hua.