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Sbornik: Mathematics, 2017, Volume 208, Issue 5, Pages 644–683
DOI: https://doi.org/10.1070/SM8718 (Mi sm8718) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The average length of finite continued fractions with fixed denominator

V. A. Bykovskiia, D. A. Frolenkovba

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (676 kB) Citations (2) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8718
Abstract: In 1968 Heilbronn proved an asymptotic formula for the mean value of the lengths of continued fraction expansions of rational numbers with identical denominators. A new method is proposed for solving Heilbronn's problem and its generalizations. New estimates for the remainders, which improve the earlier results due to Porter (1975) and Ustinov (2005), are obtained.
Bibliography: 28 titles.
Keywords: continued fraction, additive divisor problem, convolution formula.
Funding agency Grant number
Russian Science Foundation 14-11-00335
This research was financed by a grant from the Russian Science Foundation (project no. 14-11-00335) at the Khabarovsk Division of the Institute of Applied Mathematics of the Far-Eastern Branch of the Russian Academy of Sciences.
Received: 13.04.2016 and 30.11.2016
Bibliographic databases:
Document Type: Article
UDC: 517.524+511.335+517.58
MSC: 11K50
Language: English
Original paper language: Russian
Citation: V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Sb. Math., 208:5 (2017), 644–683
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM8718
  • https://www.mathnet.ru/eng/sm/v208/i5/p63
    • Related presentations:
    This publication is cited in the following 2 articles:
    1. Christoph Aistleitner, Bence Borda, Manuel Hauke, “On the distribution of partial quotients of reduced fractions with fixed denominator”, Trans. Amer. Math. Soc., 377:2 (2023), 1371  crossref  mathscinet
    2. P. Minelli, A. Sourmelidis, M. Technau, “Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums”, Math. Ann., 2022  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Statistics & downloads:
    Abstract page:844
    Russian version PDF:139
    English version PDF:74
    References:109
    First page:38
     
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