## Duke Mathematical Journal

### A density version of the Vinogradov three primes theorem

Xuancheng Shao

#### 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.

#### Article information

Source
Duke Math. J., Volume 163, Number 3 (2014), 489-512.

Dates
First available in Project Euclid: 11 February 2014

https://projecteuclid.org/euclid.dmj/1392128876

Digital Object Identifier
doi:10.1215/00127094-2410176

Mathematical Reviews number (MathSciNet)
MR3165421

Zentralblatt MATH identifier
1330.11062

#### Citation

Shao, Xuancheng. A density version of the Vinogradov three primes theorem. Duke Math. J. 163 (2014), no. 3, 489--512. doi:10.1215/00127094-2410176. https://projecteuclid.org/euclid.dmj/1392128876

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