A trigonometric approach for Chebyshev polynomials over finite fields

Juliano B. Lima, D. Panario, R. Souza
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引用次数: 8

Abstract

In this paper, we introduce trigonometric definitions for Chebyshev polynomials over finite fields Fq , where q = pm , m is a positive integer and p is an odd prime. From such definitions, we derive recurrence relations which are equivalent to those established for real valued Chebyshev polynomials and for Chebyshev polynomials of the first and second kinds over finite fields. Periodicity and symmetry properties of these polynomials are also studied. Such properties are then used to derive sufficient conditions for the Chebyshev polynomials of the second, third and fourth kinds over finite fields to be permutation polynomials.
有限域上切比雪夫多项式的三角方法
本文引入有限域Fq上切比雪夫多项式的三角函数定义,其中q = pm, m为正整数,p为奇素数。由这些定义,我们得到了等价于实值切比雪夫多项式和有限域上第一类和第二类切比雪夫多项式的递推关系。研究了这些多项式的周期性和对称性。然后利用这些性质推导出有限域上第二、三、四类切比雪夫多项式是置换多项式的充分条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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