Chebyshev Action on Finite Fields
Number Theory
2013-11-05 v3
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.
Cite
@article{arxiv.1209.4396,
title = {Chebyshev Action on Finite Fields},
author = {T. Alden Gassert},
journal= {arXiv preprint arXiv:1209.4396},
year = {2013}
}