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Publication Date:
February 2010
ISSN:
1435-5337
DOI:
10.1515/forum.2010.039

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Forum Mathematicum

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A density version of Vinogradov's three primes theorem

Hongze Li1 / Hao Pan2

1Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People's Republic of China. lihz@sjtu.edu.cn

2Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China. haopan79@yahoo.com.cn

Citation Information: Forum Mathematicum. Volume 22, Issue 4, Pages 699–714, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.039, February 2010

Publication History:
Received:
2007-11-13
Published Online:
2010-02-08

Abstract

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

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