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## Acta Arithmetica

2013 | 159 | 3 | 201-225
Tytuł artykułu

### Sums of positive density subsets of the primes

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EN
Abstrakty
EN
We show that if A and B are subsets of the primes with positive relative lower densities α and β, then the lower density of A+B in the natural numbers is at least $(1-o(1))α/(e^{γ} log log (1/β))$, which is asymptotically best possible. This improves results of Ramaré and Ruzsa and of Chipeniuk and Hamel. As in the latter work, the problem is reduced to a similar problem for subsets of $ℤ*_m$ using techniques of Green and Green-Tao. Concerning this new problem we show that, for any square-free m and any $A, B ⊆ ℤ*_m$ of densities α and β, the density of A+B in $ℤ_m$ is at least $(1-o(1))α/(e^{γ} log log (1/β))$, which is asymptotically best possible when m is a product of small primes. We also discuss an inverse question.
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Rocznik
Tom
Numer
Strony
201-225
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
• Department of Mathematics, University of Turku, 20014 Turku, Finland
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