Anne de Roton

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In this paper, we are interested in a generalization of the notion of sum-free sets. We address a conjecture first made in the 90s by Chung and Goldwasser. Recently, after some computer checks, this conjecture was formulated again by Matolcsi and Ruzsa, who made a first significant step towards it. Here, we prove the full conjecture by giving an optimal(More)
Let A be a subset of the primes. Let δP (N) = |{n ∈ A : n ≤ N}| |{n prime : n ≤ N}| . We prove that, if δP (N) ≥ C log log logN (log logN)1/3 for N ≥ N0, where C and N0 are absolute constants, then A ∩ [1, N ] contains a non-trivial three-term arithmetic progression. This improves on Green’s result [Gr], which needs δP (N) ≥ C s log log log log logN log log(More)
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