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Matematicheskie Zametki, 2016, Volume 99, Issue 2, Pages 298–308
DOI: https://doi.org/10.4213/mzm10677 (Mi mzm10677) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Estimates of the Averaged Sums of Fractional Parts

E. A. Sevast'yanov, I. Yu. Yakupov

National Engineering Physics Institute "MEPhI", Moscow
Full-text PDF (444 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm10677
Abstract: We establish asymptotically sharp estimates for the sums of the inverses (and more general sums) of the fractional parts $\{i\theta\}$ of irrational numbers $\theta$, depending on the arithmetical characteristics of the numbers $\theta$.
Keywords: averaged sum of fractional parts, irrational number, continued fraction, convergent, monotone function, Abel transformation, Khinchin's theorem.
Received: 08.04.2015
Revised: 25.04.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 2, Pages 320–329
DOI: https://doi.org/10.1134/S0001434616010351
Bibliographic databases:
Document Type: Article
UDC: 511+511.9
Language: Russian
Citation: E. A. Sevast'yanov, I. Yu. Yakupov, “Estimates of the Averaged Sums of Fractional Parts”, Mat. Zametki, 99:2 (2016), 298–308; Math. Notes, 99:2 (2016), 320–329
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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