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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 458, Pages 42–76 (Mi znsl6453)  

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

Fractional-linear invariance of multidimensional continued fractions

V. G. Zhuravlev

Vladimir State University, Vladimir, Russia
Full-text PDF (310 kB) Citations (3)
References:
Abstract: With the help of the simplex-karyon algorithm it is possible to decompose real numbers $\alpha=(\alpha_1,\dots,\alpha_d)$ into multidimensional continued fractions. We prove the invariance of this algorithm under fractional-linear transformations $\alpha'=(\alpha'_1,\dots,\alpha'_d)=U\langle\alpha\rangle$ with matrices $U$ from the unimodular group $\mathrm{GL}_{d+1}(\mathbb Z)$. The best convergent fractions of the transformed $\alpha'$ are found.
Key words and phrases: multidimensional continued fractions, the best approximations, Farey summs.
Funding agency Grant number
Russian Science Foundation 14-11-00433
Received: 05.04.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 234, Issue 5, Pages 616–639
DOI: https://doi.org/10.1007/s10958-018-4033-4
Document Type: Article
UDC: 511
Language: Russian
Citation: V. G. Zhuravlev, “Fractional-linear invariance of multidimensional continued fractions”, Analytical theory of numbers and theory of functions. Part 33, Zap. Nauchn. Sem. POMI, 458, POMI, St. Petersburg, 2017, 42–76; J. Math. Sci. (N. Y.), 234:5 (2018), 616–639
Citation in format AMSBIB
\Bibitem{Zhu17}
\by V.~G.~Zhuravlev
\paper Fractional-linear invariance of multidimensional continued fractions
\inbook Analytical theory of numbers and theory of functions. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 458
\pages 42--76
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6453}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 5
\pages 616--639
\crossref{https://doi.org/10.1007/s10958-018-4033-4}
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  • https://www.mathnet.ru/eng/znsl/v458/p42
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:31
     
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