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Sbornik: Mathematics, 2009, Volume 200, Issue 8, Pages 1181–1214
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004034 (Mi sm6367) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The average length of reduced regular continued fractions

E. N. Zhabitskaya

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (435 kB) Citations (6) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2009v200n08ABEH004034
Abstract: Let $l(a/b)$ be the number of steps of the by-excess Euclidean algorithm applied to the numbers $a$ and $b$. In this paper we obtain a three-term asymptotic formula for the expectation of the random value $l(a/b)$, when $1\le a\le b\le R$ and $R\to\infty$.
Bibliography: 11 titles.
Keywords: Euclidean algorithm, division by-excess, average length, continued fraction.
Received: 21.05.2008 and 27.03.2009
Bibliographic databases:
UDC: 511.335
MSC: Primary 11A55; Secondary 11K50
Language: English
Original paper language: Russian
Citation: E. N. Zhabitskaya, “The average length of reduced regular continued fractions”, Sb. Math., 200:8 (2009), 1181–1214
Citation in format AMSBIB
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\paper The average length of reduced regular continued fractions
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  • https://www.mathnet.ru/eng/sm/v200/i8/p79
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:459
    Russian version PDF:199
    English version PDF:8
    References:51
    First page:14
     
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