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Sbornik: Mathematics, 2007, Volume 198, Issue 5, Pages 661–690
DOI: https://doi.org/10.1070/SM2007v198n05ABEH003854 (Mi sm1436) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Partitioning of the interval $[0,1]$ induced by the Brocot sequences

A. A. Dushistova

M. V. Lomonosov Moscow State University
English version PDF (314 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2007v198n05ABEH003854
Abstract: Let $p_{i,n}$, $i=1,\dots,2^{n-1}$, be the lengths of the intervals between successive points in the Brocot sequence $F_n$. An asymptotic formula for the quantity $\sigma(F_n)=\sum_{i=1}^{N(n)}p_{i,n}^\beta$, which improves the previously known estimates, is obtained.
Bibliography: 5 titles.
Received: 10.11.2005 and 17.11.2006
Russian version:
Matematicheskii Sbornik, 2007, Volume 198, Number 5, Pages 67–94
DOI: https://doi.org/10.4213/sm1436
Bibliographic databases:
UDC: 511.216
MSC: Primary 11B99; Secondary 11J70, 37A45
Language: English
Original paper language: Russian
Citation: A. A. Dushistova, “Partitioning of the interval $[0,1]$ induced by the Brocot sequences”, Mat. Sb., 198:5 (2007), 67–94; Sb. Math., 198:5 (2007), 661–690
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:194
    English version PDF:5
    References:44
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