13 citations · 20 across the 5 of their papers we have counts for
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Long arithmetic progressions of primes
Ben Green
This is an article for a general mathematical audience on the author's work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes.…
Freiman's Theorem in an arbitrary abelian group
Ben Green, Imre Z. Ruzsa
A famous result of Freiman describes the structure of finite sets A of integers with small doubling property. If |A + A| <= K|A| then A is contained within a multidimensional arith…
Finite field models in additive combinatorics
Ben Green
The study of many problems in additive combinatorics, such as Szemerédi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for s…
Restriction theory of the Selberg sieve, with applications
Ben Green, Terence Tao
The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an L^2-L^p restriction theorem for majorants of this type. A…
Sets with small sumset and rectification
Ben Green, Imre Z. Ruzsa
We study the extent to which sets A in Z/NZ, N prime, resemble sets of integers from the additive point of view (``up to Freiman isomorphism''). We give a direct proof of a result…