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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
Nom de la revue
Functional Analysis and its Applications
Volume
38
Numéro
1
Éditeur
Springer
Pages
1-13
Identifiant publication
Métadonnées
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Auteur(s)
Arnold, Vladimir
Résumé (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.
Mots-clés
arithmetics; symmetric function; trace; de Sitter world; Fermat's little theorem; Lobachevsky geometry; Kepler cube; Riemann surface