A density version of Vinogradov's three primes theorem

作者:Li, Hongze*; Pan, Hao
来源:Forum Mathematicum, 2010, 22(4): 699-714.
DOI:10.1515/FORUM.2010.039

摘要

Let P denote the set of all primes. Suppose that P(1), P(2), P(3) are three subsets of P with (d) under bar (P)(P(1)) (d) under bar (P)(P(2)) (d) under bar (P)(P(3)) > 2, where (d) under barP(P(i)) is the lower density of P(i) relative to P. We prove that for every sufficiently large odd integer n, there exist p(i) is an element of P(i) such that n = p(1) p(2) p(3).