Chebyshev action on finite fields

被引：24

作者：

Gassert, T. Alden ^{[1
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

来源：

DISCRETE MATHEMATICS | 2014年 / 315卷

关键词：

Chebyshev polynomial; Iterated polynomial; Post-critically finite map; Finite field; Prime decomposition;

D O I：

10.1016/j.disc.2013.10.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a polynomial phi(x) and a finite field F-q 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 phi. When phi 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 then use these graphs to determine the decomposition of primes in the Chebyshev radical extensions. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：83 / 94

页数：12

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