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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)
References:
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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:
    1. Swee Hong Chan, Igor Pak, “Linear extensions and continued fractions”, European Journal of Combinatorics, 122 (2024), 104018  crossref
    2. A. A. Illarionov, “Veroyatnostnye otsenki, svyazannye s teoretiko-chislovymi kvadraturnymi formulami Korobova”, Algebra i analiz, 36:6 (2024), 47–81  mathnet
    3. 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
    4. A. A. Illarionov, “Distribution of Korobov-Hlawka sequences”, Sb. Math., 213:9 (2022), 1222–1249  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Radosław Żak, “Finding binary words with a given number of subsequences”, Theoretical Computer Science, 919 (2022), 75  crossref
    6. A. A. Illarionov, “A probability estimate for the discrepancy of Korobov lattice points”, Sb. Math., 212:11 (2021), 1571–1587  mathnet  crossref  crossref  zmath  adsnasa  isi
    7. Moshchevitin N., Murphy B., Shkredov I., “Popular Products and Continued Fractions”, Isr. J. Math., 238:2 (2020), 807–835  crossref  mathscinet  isi  scopus
    8. A. A. Illarionov, “O raspredelenii tselochislennykh dlin reber poliedrov Kleina”, Dalnevost. matem. zhurn., 15:2 (2015), 214–221  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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