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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
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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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    References:94
    First page:38
     
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