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Counting irreducible polynomials over finite fields

Qichun Wang, Haibin Kan (2010)

Czechoslovak Mathematical Journal

In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: π ( x ) = q q - 1 x log q x + q ( q - 1 ) 2 x log q 2 x + O x log q 3 x , x = q n where π ( x ) denotes the number of monic irreducible polynomials in F q [ t ] with norm x .

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