Page 1

Displaying 1 – 6 of 6

Showing per page

Character sums in complex half-planes

Sergei V. Konyagin, Vsevolod 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 .

Characterization of power digraphs modulo n

Uzma Ahmad, Syed Husnine (2011)

Commentationes Mathematicae Universitatis Carolinae

A power digraph modulo n , denoted by G ( n , k ) , is a directed graph with Z n = { 0 , 1 , , n - 1 } as the set of vertices and E = { ( a , b ) : a k b ( mod n ) } as the edge set, where n and k are any positive integers. In this paper we find necessary and sufficient conditions on n and k such that the digraph G ( n , k ) has at least one isolated fixed point. We also establish necessary and sufficient conditions on n and k such that the digraph G ( n , k ) contains exactly two components. The primality of Fermat number is also discussed.

Completing codes

A. Restivo, S. Salemi, T. Sportelli (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Complex Hadamard matrices and the spectral set conjecture.

Mihail N. Kolountzakis, Máté Matolcsi (2006)

Collectanea Mathematica

By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.

Currently displaying 1 – 6 of 6

Page 1