On Sums of Sets of Primes with Positive Relative Density

Details On Sums of Sets of Primes with Positive Relative Density On Sums of Sets of Primes with Positive Relative Density

2009-12-24

arxiv.org/abs/0912.4910v2

Mathematics

Number Theory

21 pages, to appear in J. London Math. Soc., short remark added and typos fixed

Scientific paper

In this paper we show that if $A$ is a subset of the primes with positive relative density $\delta$, then $A+A$ must have positive upper density $C_1\delta e^{-C_2(\log(1/\delta))^{2/3}(\log\log(1/\delta))^{1/3}}$ in $\mathbb{N}$. Our argument applies the techniques developed by Green and Green-Tao used to find arithmetic progressions in the primes, in combination with a result on sums of subsets of the multiplicative subgroup of the integers modulo $M$.

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