In this paper we enumerate irreducible polynomials of degree m and related objects over a finite field ${\mathbb{F}}_q$ with respect to their trace and norm. Our approach makes use of both generating functions and exponential sums, and we improve all previously known results in the literature when $m>\sqrt{q}$.

中文翻译：

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关于有限域上不可约多项式和相关对象的迹和范数的枚举

在本文中，我们枚举了有限域上m级的不可约多项式及相关对象${\mathbb{F}}_q$关于他们的踪迹和规范。我们的方法同时利用了生成函数和指数和，并且我们改进了文献中所有先前已知的结果。$米>\sqrt{q}$。