An Additive Problem with Piatetski-Shapiro Primes and Almost-Primes

摘要

Suppose that . We prove a theorem of Bombieri-Vinogradov type for the Piatetski-Shapiro primes p = [n 1/γ and show that every sufficiently large even integer can be written as a sum of a Piatetski-Shapiro prime and an almost-prime.