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

Arnold, Vladimir (2004), Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes, Functional Analysis and its Applications, 38, 1, p. 1-13. http://dx.doi.org/10.1023/B:FAIA.0000024863.06462.68

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Functional Analysis and its Applications
Volume
38
Number
1
Publisher
Springer
Pages
1-13
Publication identifier
Metadata
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Author(s)
Arnold, Vladimir
Abstract (EN)
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.
Subjects / Keywords
arithmetics; symmetric function; trace; de Sitter world; Fermat's little theorem; Lobachevsky geometry; Kepler cube; Riemann surface