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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 1, Pages 1–15
DOI: https://doi.org/10.4213/faa92 (Mi faa92) 		 
This article is cited in 15 scientific papers (total in 16 papers)

Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes

V. I. Arnol'dab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paris-Dauphine
Full-text PDF (215 kB) Citations (16)
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DOI: https://doi.org/10.4213/faa92
Abstract: Congruences generalizing Fermat's little theorem are proved for the traces of powers of integer matrices. Their relations to Lobachevsky geometries over finite fields and combinatorics of the matrix squaring operation as well as to the corresponding Riemann surfaces with their Kepler cubes are discussed.
Keywords: arithmetics, symmetric function, de Sitter world, trace, Fermat's little theorem, Lobachevsky geometry, Kepler cube, Riemann surface.
Received: 03.10.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 1, Pages 1–13
DOI: https://doi.org/10.1023/B:FAIA.0000024863.06462.68
Bibliographic databases:
Document Type: Article
UDC: 51
Language: Russian
Citation: V. I. Arnol'd, “Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 1–15; Funct. Anal. Appl., 38:1 (2004), 1–13
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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