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

摘要

Suppose that (662)/(755) < γ < 1. 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.