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Dal'nevost. Mat. Zh., 2011, Volume 11, Number 1, Pages 93–98 (Mi dvmg214)  

This article is cited in 3 scientific papers (total in 3 papers)

On Gauss — Kuz'min statistics in short intervals

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The article is devoted to investigation of Gauss — Kuz'min statistics for rational numbers $a/b$, where $b$ is fixed, $1\le a\le b$, $(a,b)=1$. New asymptotic formula for the mean value of Gauss — Kuz'min statistics is proved. It sharpens previous result which is similar to the Porter's theorem.

Key words: Euclidean algorithm, continued fractions, Kloosterman sums, Gauss — Kuz'min statistics

Full text: PDF file (202 kB)
References: PDF file   HTML file
UDC: 511.37, 511.336
MSC: Primary 11L05; Secondary 11Y16
Received: 01.11.2010

Citation: A. V. Ustinov, “On Gauss — Kuz'min statistics in short intervals”, Dal'nevost. Mat. Zh., 11:1 (2011), 93–98

Citation in format AMSBIB
\Bibitem{Ust11}
\by A.~V.~Ustinov
\paper On Gauss~--- Kuz'min statistics in short intervals
\jour Dal'nevost. Mat. Zh.
\yr 2011
\vol 11
\issue 1
\pages 93--98
\mathnet{http://mi.mathnet.ru/dvmg214}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Bykovskii V.A., Frolenkov D.A., “Asymptotic Formula For the Convolution of a Generalized Divisor Function”, Dokl. Math., 92:3 (2015), 670–673  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Sb. Math., 208:5 (2017), 644–683  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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