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1
Content available remote

Distribution of lattice points on hyperbolic surfaces

100%
Lev V.
Acta Arithmetica
|
1996
|
tom 75
|
nr 1
85-95
EN
Let two lattices $Λ', Λ'' ⊂ ℝ^s$ have the same number of points on each hyperbolic surface $|x₁...x_s| = C$. We investigate the case when Λ', Λ'' are sublattices of $ℤ^s$ of the same prime index and show that then Λ' and Λ'' must coincide up to renumbering the coordinate axes and changing their directions.
2
Content available remote

Blocks and progressions in subset sum sets

88%
Lev V.
Acta Arithmetica
|
2003
|
tom 106
|
nr 2
123-142
3
Content available remote

Powers of 2 with five distinct summands

88%
Lev V.
Acta Arithmetica
|
2008
|
tom 132
|
nr 3
197-204
4
Content available remote

Solving a ± b = 2c in elements of finite sets

64%
Lev V., Pinchasi R.
Acta Arithmetica
|
2014
|
tom 163
|
nr 2
127-140
EN
We show that if A and B are finite sets of real numbers, then the number of triples (a,b,c) ∈ A × B × (A ∪ B) with a + b = 2c is at most (0.15+o(1))(|A|+|B|)² as |A| + |B| → ∞. As a corollary, if A is antisymmetric (that is, A ∩ (-A) = ∅), then there are at most (0.3+o(1))|A|² triples (a,b,c) with a,b,c ∈ A and a - b = 2c. In the general case where A is not necessarily antisymmetric, we show that the number of triples (a,b,c) with a,b,c ∈ A and a - b = 2c is at most (0.5+o(1))|A|². These estimates are sharp.
5
Content available remote

On addition of two distinct sets of integers

64%
Lev V., Smeliansky P.
Acta Arithmetica
|
1995
|
tom 70
|
nr 1
85-91
EN
What is the structure of a pair of finite integers sets A,B ⊂ ℤ with the small value of |A+B|? We answer this question for addition coefficient 3. The obtained theorem sharpens the corresponding results of G. Freiman.
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