In this paper, we first introduce a trigonometric approach for Dickson polynomials of the first and the second kinds over fields of characteristic two. Employing the proposed concepts, we revisit known properties of such polynomials. Additionally, we derive new results regarding the fixed points and the involutive behavior of Dickson polynomials of the second kind over $${\mathbb {F}}_{2^n}$$ F 2 n .

中文翻译：

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特征二域上 Dickson 多项式的三角方法

在本文中，我们首先介绍了在特征二域上的第一类和第二类 Dickson 多项式的三角方法。利用所提出的概念，我们重新审视此类多项式的已知属性。此外，我们推导出关于不动点和第二类 Dickson 多项式在 $${\mathbb {F}}_{2^n}$$ F 2 n 上的对合行为的新结果。