Let ${\mathbb{F}}_q$ be the finite field with q elements, and T a positive integer. In this article, we find an asymptotic formula for the total number of monic irreducible binomials in ${\mathbb{F}}_q[x]$ of degree less or equal to T, when T is large enough. We also show explicit lower and upper bounds for the number of binomials in the case when T is small.

中文翻译：

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不可约二项式的估计数量

让 ${\mathbb{F}}_q$是具有q个元素的有限域，T是一个正整数。在本文中，我们找到了一个不可约二项式总和的渐近公式${\mathbb{F}}_q[X]$当T足够大时，其度数小于或等于T。在T较小的情况下，我们还显示了二项式数的显式上下限。