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Uniform distribution and Voronoń≠ convergence. (English) Zbl 1142.11342
Sb. Math. 196, No. 10, 1495-1502 (2005); translation from Mat. Sb. 196, No. 10, 103-110 (2005).
The author obtains sufficient conditions for a sequence to be Voronoi uniformly distributed in the unit interval. For an integer \(a\geq 2\) he proves that the sequence of fractional parts \(\left\{\frac{1}{2}\log_an\right\}\) is not Voronoi uniformly distributed, for every regular Voronoi summation method.

MSC:
11J71 Distribution modulo one
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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