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Matematicheskie Zametki, 2011, Volume 90, Issue 3, Pages 431–444
DOI: https://doi.org/10.4213/mzm8484 (Mi mzm8484) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator

M. G. Rukavishnikovaab

a Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
b Far-Eastern State University of Humanities
Full-text PDF (491 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm8484
Abstract: We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients.
Keywords: law of large numbers, rational number, continued fraction, partial quotient, Euler function, Möbius function, Riemann zeta function.
Received: 12.02.2009
Revised: 04.12.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 3, Pages 418–430
DOI: https://doi.org/10.1134/S0001434611090100
Bibliographic databases:
Document Type: Article
UDC: 511.36+511.37
Language: Russian
Citation: M. G. Rukavishnikova, “The Law of Large Numbers for the Sum of the Partial Quotients of a Rational Number with Fixed Denominator”, Mat. Zametki, 90:3 (2011), 431–444; Math. Notes, 90:3 (2011), 418–430
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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