Displaying similar documents to “Mean square limit for lattice points in a sphere”

On the structure of sets with small doubling property on the plane (I)

Yonutz Stanchescu (1998)

Acta Arithmetica

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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.