Displaying similar documents to “On the Poincaré series for diagonal forms over algebraic number fields”

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.