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Matematicheskie Zametki, 2010, Volume 88, Issue 1, Pages 30–42
DOI: https://doi.org/10.4213/mzm4045 (Mi mzm4045) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators

O. N. Karpenkov

Mathematical Institute, Leiden University
Full-text PDF (578 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm4045
Abstract: An explicit construction of a reduced hyperbolic integer operator from the group $SL(2,\mathbb Z)$ such that one of the periods of the corresponding geometric continued fraction in the sense of Klein coincides with a given sequence of positive integers is presented. An algorithm determining periods for any operator in $SL(2,\mathbb Z)$ (which is based on Gauss' reduction theory) is experimentally studied.
Keywords: geometric continued fraction in the sense of Klein, period of a geometric continued fraction, hyperbolic integer operator, sail of an integer operator, LLS-sequence, integer length, integer sine.
Received: 26.09.2007
English version:
Mathematical Notes, 2010, Volume 88, Issue 1, Pages 28–38
DOI: https://doi.org/10.1134/S0001434610070035
Bibliographic databases:
Document Type: Article
UDC: 511.48
Language: Russian
Citation: O. N. Karpenkov, “Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators”, Mat. Zametki, 88:1 (2010), 30–42; Math. Notes, 88:1 (2010), 28–38
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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