Geodesic
Counting irreducible polynomials over finite fields
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 881-886

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: \[ \pi (x)= \frac q{q - 1}\frac x{{\log _q x}}+ \frac q{(q - 1)^2}\frac x{{\log _q^2 x}}+O\Bigl (\frac {x}{{\log _q^3 x}}\Bigr ),\quad x=q^n\rightarrow \infty \] where $\pi (x)$ denotes the number of monic irreducible polynomials in $F_q [t]$ with norm $ \le x$.
Classification : 11T55
Keywords: finite fields; distribution of irreducible polynomials; residue 
@article{CMJ_2010__60_3_a18,
     author = {Wang, Qichun and Kan, Haibin},
     title = {Counting irreducible polynomials over finite fields},
     journal = {Czechoslovak Mathematical Journal},
     pages = {881--886},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2010},
     mrnumber = {2672421},
     zbl = {1224.11086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a18/}
}
TY  - JOUR
AU  - Wang, Qichun
AU  - Kan, Haibin
TI  - Counting irreducible polynomials over finite fields
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 881
EP  - 886
VL  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a18/
LA  - en
ID  - CMJ_2010__60_3_a18
ER  - 
%0 Journal Article
%A Wang, Qichun
%A Kan, Haibin
%T Counting irreducible polynomials over finite fields
%J Czechoslovak Mathematical Journal
%D 2010
%P 881-886
%V 60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a18/
%G en
%F CMJ_2010__60_3_a18
Wang, Qichun; Kan, Haibin. Counting irreducible polynomials over finite fields. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 881-886. http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a18/