Geodesic
Uniform distribution and Voronoi convergence
Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1495-1502 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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