Generating series for irreducible polynomials over finite fields

We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the case of the multi-degree and the case of indecomposable polynomials.

• Type: Journal
• Year: 2010
• Where: FFA
• Authors: Arnaud Bodin
• Keywords: Exact Formula, FFA 2010, Irreducible Polynomials, finite field