RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2016, Volume 99, Issue 1, Pages 26–34 (Mi mz10852)  

An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers

E. B. Borodina

Lomonosov Moscow State University

Abstract: The Güting algorithm for constructing multidimensional continued fractions is considered. It is proved that, in the case of dimension $2$, this algorithm can be used to find the coefficients of the linear dependence of numbers; a criterion is given for verifying that the partial quotients furnished by the algorithm are, indeed, elements of the continued fraction for the expanded (generally irrational) numbers.

Keywords: multidimensional continued fraction, Güting algorithm, linear dependence of numbers, partial quotient, irrational number.

Funding Agency Grant Number
Russian Foundation for Basic Research 09-01-00743


DOI: https://doi.org/10.4213/mzm10852

Full text: PDF file (424 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2016, 99:1, 37–45

Bibliographic databases:

UDC: 511
Received: 05.08.2012
Revised: 17.06.2015

Citation: E. B. Borodina, “An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers”, Mat. Zametki, 99:1 (2016), 26–34; Math. Notes, 99:1 (2016), 37–45

Citation in format AMSBIB
\Bibitem{Bor16}
\by E.~B.~Borodina
\paper An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers
\jour Mat. Zametki
\yr 2016
\vol 99
\issue 1
\pages 26--34
\mathnet{http://mi.mathnet.ru/mz10852}
\crossref{https://doi.org/10.4213/mzm10852}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3462685}
\elib{http://elibrary.ru/item.asp?id=25707638}
\transl
\jour Math. Notes
\yr 2016
\vol 99
\issue 1
\pages 37--45
\crossref{https://doi.org/10.1134/S0001434616010041}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000373228900004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962469273}


Linking options:
  • http://mi.mathnet.ru/eng/mz10852
  • https://doi.org/10.4213/mzm10852
  • http://mi.mathnet.ru/eng/mz/v99/i1/p26

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:160
    Full text:40
    References:46
    First page:33

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020