Weighted averages, uniform distribution, and strict ergodicity

V. V. Kozlov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1121-1146

Résumé

A circle of problems related to the application of the Riesz and Voronoi summation methods in ergodic theory, number theory, and probability theory is considered. The first digit paradox is discussed, strengthenings of the classical result of Weyl on the uniform distribution of the fractional parts of the values of a polynomial are indicated, and the possibility of sharpening the Birkhoff–Khinchin ergodic theorem is considered. In conclusion, some unsolved problems are listed.

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