Chebyshev Action on Finite Fields

2012/09/20 by T. Alden Gassert, Gassert, T. Alden · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #Graph theory and applications #math.NT

paper · pdf · doi:10.48550/arxiv.1209.4396

arxiv created 2013/11/03 · arxiv updated 2013/11/05

Abstract

Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f. When f is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry. In this paper we provide a complete description of these graphs, and also provide some examples of how these graphs can be used to determine the decomposition of primes in certain field extensions.

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• Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields

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