A generalization of the Goldbach-Vinogradov theorem

Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.

Sur la densité de certains ensembles de multiples, 2

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Acta Arithmetica

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Séminaire Lotharingien de Combinatoire [electronic only]

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