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Dal'nevost. Mat. Zh., 2011, Volume 11, Number 1, Pages 10–27 (Mi dvmg207)  

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

The average length of Minkowski's diagonal continued fractions

O. A. Gorkusha

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

Abstract: We prove asymptotic formulae with two significant terms for the expectation of the random variable $s(c/d;1)$ — length of Minkowski's diagonal continued fraction when the variables $c$ and $d$ range over the set $1\le c\le d\le R<\infty$.

Key words: Continued fractions, geometry of numbers, lattices

Full text: PDF file (279 kB)
References: PDF file   HTML file
UDC: 511.9
MSC: Primary 11D68; Secondary 11D85
Received: 01.07.2010

Citation: O. A. Gorkusha, “The average length of Minkowski's diagonal continued fractions”, Dal'nevost. Mat. Zh., 11:1 (2011), 10–27

Citation in format AMSBIB
\Bibitem{Gor11}
\by O.~A.~Gorkusha
\paper The average length of Minkowski's diagonal continued fractions
\jour Dal'nevost. Mat. Zh.
\yr 2011
\vol 11
\issue 1
\pages 10--27
\mathnet{http://mi.mathnet.ru/dvmg207}
\elib{https://elibrary.ru/item.asp?id=16214053}


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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
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