A Density Version of the Vinogradov Three Primes Theorem

Abstract

We prove that if A is a subset of the primes, and the lower density of A in the primes is larger than 5/8, then all sufficiently large odd positive integers can be written as the sum of three primes in A. The constant 5/8 in this statement is the best possible.

17 pages. To appear in Duke Math Journal. This is the final version, incorporating referee's suggestions

References in corpus (2)

• Minor arcs for Goldbach's problem
• A New Proof of Vinogradov's Three Primes Theorem

Cited by in corpus (9)

• The ternary Goldbach conjecture is true
• Minor arcs for Goldbach's problem
• Vinogradov's theorem with almost equal summands
• A Density version of Waring's problem
• Vinogradov's Theorem with Fouvry-Iwaniec Primes
• Vinogradov's three primes theorem with primes having given primitive roots
• A New Proof of Vinogradov's Three Primes Theorem
• A transference principle for systems of linear equations, and applications to almost twin primes
• Products of primes in arithmetic progressions