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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 1, Pages 51–66 (Mi izv1135)  

This article is cited in 8 scientific papers (total in 8 papers)

On a multidimensional generalization of Lagrange's theorem on continued fractions

O. N. Germana, E. L. Lakshtanovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Aveiro

Abstract: We prove a multidimensional analogue of the classical Lagrange theorem on continued fractions using Klein polyhedra as a multidimensional generalization of continued fractions.

DOI: https://doi.org/10.4213/im1135

Full text: PDF file (600 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2008, 72:1, 47–61

Bibliographic databases:

UDC: 511.6+511.9
MSC: 11H06, 11H46, 11H50
Received: 12.07.2006

Citation: O. N. German, E. L. Lakshtanov, “On a multidimensional generalization of Lagrange's theorem on continued fractions”, Izv. RAN. Ser. Mat., 72:1 (2008), 51–66; Izv. Math., 72:1 (2008), 47–61

Citation in format AMSBIB
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  • https://doi.org/10.4213/im1135
  • http://mi.mathnet.ru/eng/izv/v72/i1/p51

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Bykovskaya, “A Multidimensional Generalization of Lagrange's Theorem on Continued Fractions”, Math. Notes, 92:3 (2012), 312–326  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. V. Bykovskaya, “A Criterion for the Integral Equivalence of Two Generalized Convex Integer Polyhedra”, Math. Notes, 94:5 (2013), 609–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. O. N. German, “Plokho priblizhaemye matritsy i diofantovy eksponenty”, Chebyshevskii sb., 14:4 (2013), 38–79  mathnet
    4. I. A. Makarov, “Interior Klein Polyhedra”, Math. Notes, 95:6 (2014), 795–805  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Drouin Ch., “A Two-Dimensional Continued Fraction Algorithm With Lagrange and Dirichlet Properties”, J. Theor. Nr. Bordx., 26:2 (2014), 307–346  crossref  mathscinet  zmath  isi  scopus
    6. A. A. Illarionov, “Some properties of three-dimensional Klein polyhedra”, Sb. Math., 206:4 (2015), 510–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Murru N., “Linear Recurrence Sequences and Periodicity of Multidimensional Continued Fractions”, Ramanujan J., 44:1 (2017), 115–124  crossref  mathscinet  zmath  isi  scopus
    8. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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