Currently displaying 1 – 12 of 12

Showing per page

Order by Relevance | Title | Year of publication

Distribution of lattice points on hyperbolic surfaces

Vsevolod F. Lev — 1996

Acta Arithmetica

Let two lattices Λ ' , Λ ' ' s have the same number of points on each hyperbolic surface | x . . . x s | = C . We investigate the case when Λ’, Λ” are sublattices of 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.

Restricted set addition in Abelian groups: results and conjectures

Vsevolod F. Lev — 2005

Journal de Théorie des Nombres de Bordeaux

We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed. The paper assumes no expertise from the reader and can serve as an introduction to the subject.

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

Vsevolod F. LevRom Pinchasi — 2014

Acta Arithmetica

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...

Character sums in complex half-planes

Sergei V. KonyaginVsevolod F. Lev — 2004

Journal de Théorie des Nombres de Bordeaux

Let A be a finite subset of an abelian group G and let P be a closed half-plane of the complex plane, containing zero. We show that (unless A possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of A which belongs to P . In other words, there exists a non-trivial character χ G ^ such that a A χ ( a ) P .

Page 1

Download Results (CSV)