The estimated number of irreducible binomials

摘要

Let 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 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. (C) 2020 Elsevier Inc. All rights reserved.