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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 469, Pages 96–137 (Mi znsl6607)  
This article is cited in 1 scientific paper (total in 1 paper)

Unimodular invariance of karyon decompositions of algebraic numbers in multidimensional continued fractions

V. G. Zhuravlevab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Vladimir State University, Vladimir, Russia
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Abstract: By the differentiation method of induced toric tilins we find periodic expansions for algebraic irrationalities in multidimensional continued fractions. These expansions give the best karyon approximations with respect to polyhedral norms. The above irrationalities are obtained by the composition of backward continued fraction mappings and unimodular transformations of algebraic units that decompose into a purely periodic continued fractions. The artifact of this expansion several invariants has become: recurrence relations for numerators and denominators of convergent fractions and the rate of multidimensional approximation of irrationalities by rational numbers.
Key words and phrases: induced toric tilings, the best multidimensional approximations, the Lagrange theorem.
Funding agency Grant number
Russian Science Foundation 14-11-00433
Received: 06.03.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 242, Issue 4, Pages 531–559
DOI: https://doi.org/10.1007/s10958-019-04494-5
Bibliographic databases:
Document Type: Article
UDC: 511.3
Language: Russian
Citation: V. G. Zhuravlev, “Unimodular invariance of karyon decompositions of algebraic numbers in multidimensional continued fractions”, Algebra and number theory. Part 1, Zap. Nauchn. Sem. POMI, 469, POMI, St. Petersburg, 2018, 96–137; J. Math. Sci. (N. Y.), 242:4 (2019), 531–559
Citation in format AMSBIB
\Bibitem{Zhu18}
\by V.~G.~Zhuravlev
\paper Unimodular invariance of karyon decompositions of algebraic numbers in multidimensional continued fractions
\inbook Algebra and number theory. Part~1
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 469
\pages 96--137
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6607}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3885097}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 242
\issue 4
\pages 531--559
\crossref{https://doi.org/10.1007/s10958-019-04494-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85072127269}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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