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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 12, Pages 94–101 (Mi ivm9423)  

Nonautonomous bounded remainder sets

A. V. Shutov

Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin str., Moscow, 119991 Russia

Abstract: Nonautonomous bounded remainder sets are sequences of sets admitting a uniform estimate of the remainder term in the distribution of the fractional parts of linear function problem. In the paper we give a complete description of nonautonomous bounded remainder sets in the case of periodic sequences. The result is also generalized to certain classes of quasiperiodic sequences of sets. The proofs are based on obtaining explicit formulas for the remainder term in the terms of sums of fractional parts. The method is effective, i. e., it allows us to obtain explicit estimates of the remainder term.

Keywords: uniform distribution, bounded remainder set, sums of fractional parts.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
Supported by the Russian Scientific Foundation, grant No. 14-11-00433.


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English version:
Russian Mathematics, 2018, 62:12, 81–87

Bibliographic databases:

UDC: 511.431
Received: 02.11.2017

Citation: A. V. Shutov, “Nonautonomous bounded remainder sets”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 12, 94–101; Russian Mathematics, 62:12 (2018), 81–87

Citation in format AMSBIB
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\pages 81--87
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