Generating series for irreducible polynomials over finite fields

Authors:
Arnaud Bodin
Affiliations:
Laboratoire Paul Painlevé, Mathématiques, Université Lille 1, 59655 Villeneuve d'Ascq, France
Venue:
Finite Fields and Their Applications
Year:
2010

Citing 4
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Abstract

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.