On existence conditions for sequences uniformly distributed with respect to Voronoi's methods

Necessary and sufficient conditions for the uniformly distributed sequences of complex numbers with respect to Voronoi and Riesz methods have been analyzed. These conditions are necessary and sufficient for the Voronoi and Riesz methods to be regular, for the convergence of the given sequence to a finite limit to imply the convergence of Voronoi and Riesz means, respectively, to the same limit. For a sequence of ones, the methods of Voronoi and Riesz coincide with the classical methods of Cesaro's arithmetic means. A weight sequence was constructed such that both necessary and sufficient conditions hold.