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Mat. Zametki, 2011, Volume 90, Issue 3, Pages 431–444 (Mi mz8484)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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

DOI: https://doi.org/10.4213/mzm8484

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English version:
Mathematical Notes, 2011, 90:3, 418–430

Bibliographic databases:

UDC: 511.36+511.37
Received: 12.02.2009
Revised: 04.12.2010

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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\jour Mat. Zametki
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\pages 431--444
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\jour Math. Notes
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\pages 418--430
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    This publication is cited in the following articles:
    1. A. A. Illarionov, “O raspredelenii tselochislennykh dlin reber poliedrov Kleina”, Dalnevost. matem. zhurn., 15:2 (2015), 214–221  mathnet  elib
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