Generating series for irreducible polynomials over finite fields
classification
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polynomialscasefinitegeneratingirreducibleseriesapproximationasymptotic
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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.
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