Geodesic
Uniform distribution and Voronoi convergence
Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1495-1502

Voir la notice de l'article provenant de la source Math-Net.Ru

There is a broad generalization of a uniformly distributed sequence according to Weyl where the frequency of elements of this sequence falling into an interval is defined by using a matrix summation method of a general form. In the present paper conditions for uniform distribution are found in the case where a regular Voronoi method is chosen as the summation method. The proofs are based on estimates of trigonometric sums of a certain special type. It is shown that the sequence of the fractional parts of the logarithms of positive integers is not uniformly distributed for any choice of a regular Voronoi method. 
@article{SM_2005_196_10_a3,
     author = {V. V. Kozlov and T. V. Madsen},
     title = {Uniform distribution and {Voronoi} convergence},
     journal = {Sbornik. Mathematics},
     pages = {1495--1502},
     publisher = {mathdoc},
     volume = {196},
     number = {10},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_10_a3/}
}
TY  - JOUR
AU  - V. V. Kozlov
AU  - T. V. Madsen
TI  - Uniform distribution and Voronoi convergence
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 1495
EP  - 1502
VL  - 196
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_10_a3/
LA  - en
ID  - SM_2005_196_10_a3
ER  - 
%0 Journal Article
%A V. V. Kozlov
%A T. V. Madsen
%T Uniform distribution and Voronoi convergence
%J Sbornik. Mathematics
%D 2005
%P 1495-1502
%V 196
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2005_196_10_a3/
%G en
%F SM_2005_196_10_a3
V. V. Kozlov; T. V. Madsen. Uniform distribution and Voronoi convergence. Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1495-1502. http://geodesic.mathdoc.fr/item/SM_2005_196_10_a3/