| Title:
|
Counting irreducible polynomials over finite fields (English) |
| Author:
|
Wang, Qichun |
| Author:
|
Kan, Haibin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
881-886 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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$. (English) |
| Keyword:
|
finite fields |
| Keyword:
|
distribution of irreducible polynomials |
| Keyword:
|
residue |
| MSC:
|
11T55 |
| idZBL:
|
Zbl 1224.11086 |
| idMR:
|
MR2672421 |
| . |
| Date available:
|
2010-07-20T17:24:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140610 |
| . |
| Reference:
|
[1] Kruse, M., Stichtenoth, H.: Ein Analogon zum Primzahlsatz fur algebraische Functionenkoper.Manuscripta Math. 69 (1990), 219-221 German. MR 1078353, 10.1007/BF02567920 |
| Reference:
|
[2] Davenport, H.: Multiplicative Number Theory.Springer-Verlag New York (1980). Zbl 0453.10002, MR 0606931 |
| . |
