Counting irreducible polynomials over finite fields

Title:

Counting irreducible polynomials over finite fields

Creator:

Wang, Qichun and Kan, Haibin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:712502a1-001c-48ef-ab1c-ce0be40593db
uuid:712502a1-001c-48ef-ab1c-ce0be40593db

Subject:

finite fields, distribution of irreducible polynomials, and residue

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

881-886

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:3

Harvested from:

CDK

Metadata only:

false