Counting irreducible polynomials over finite fields

Wang, Qichun, and Kan, Haibin. "Counting irreducible polynomials over finite fields." Czechoslovak Mathematical Journal 60.3 (2010): 881-886. <http://eudml.org/doc/38047>.

@article{Wang2010,
abstract = {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$.},
author = {Wang, Qichun, Kan, Haibin},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite fields; distribution of irreducible polynomials; residue; finite fields; distribution of irreducible polynomials; residue},
language = {eng},
number = {3},
pages = {881-886},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Counting irreducible polynomials over finite fields},
url = {http://eudml.org/doc/38047},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Wang, Qichun
AU - Kan, Haibin
TI - Counting irreducible polynomials over finite fields
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 881
EP - 886
AB - 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$.
LA - eng
KW - finite fields; distribution of irreducible polynomials; residue; finite fields; distribution of irreducible polynomials; residue
UR - http://eudml.org/doc/38047
ER -