On enumeration of irreducible polynomials and related objects over a finite field with respect to their trace and norm

In this paper we enumerate irreducible polynomials of degree m and related objects over a finite field 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 > root q. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper enumerates irreducible polynomials of degree m and related objects over a finite field F-q with respect to their trace and norm, using generating functions and exponential sums. It improves upon all previously known results in the literature when m > root q.