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Russian Mathematical Surveys, 2005, Volume 60, Issue 6, Pages 1121–1146
DOI: https://doi.org/10.1070/RM2005v060n06ABEH004284 (Mi rm1679) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Weighted averages, uniform distribution, and strict ergodicity

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (295 kB) Citations (10)
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DOI: https://doi.org/10.1070/RM2005v060n06ABEH004284
Abstract: 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.
Received: 17.08.2005
Russian version:
Uspekhi Matematicheskikh Nauk, 2005, Volume 60, Issue 6(366), Pages 115–138
DOI: https://doi.org/10.4213/rm1679
Bibliographic databases:
Document Type: Article
UDC: 510.6+519.21
MSC: Primary 40G05, 11K06, 37A30; Secondary 60F15
Language: English
Original paper language: Russian
Citation: V. V. Kozlov, “Weighted averages, uniform distribution, and strict ergodicity”, Uspekhi Mat. Nauk, 60:6(366) (2005), 115–138; Russian Math. Surveys, 60:6 (2005), 1121–1146
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v60/i6/p115
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Russian version PDF:363
    English version PDF:33
    References:87
    First page:7
     
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