このエントリーをはてなブックマークに追加
ID 14079
JaLCDOI
Sort Key
1
フルテキストURL
著者
Nogami, Yasuyuki The Graduate School of Natural Science and Technology Okayama University
Morikawa, Yoshitaka The Graduate School of Natural Science and Technology Okayama University
抄録
In this paper, we first show the number of x's such that x(2) +u, u ∈ F(*)(p) , becomes a quadratic residue in F(p), and then this number is proven to be equal to (p+1)/2 if −u is a quadratic residue in Fp, which is a necessary fact for the following. With respect to the irreducible cubic polynomials over Fp in the form of x(3)+ax+b, we give a classification based on the trace of an element in F(p3) and based on whether or not the coefficient of x, i.e. the parameter a, is a quadratic residue in Fp. According to this classification, we can know the minimal set of the irreducible cubic polynomials, from which all the irreducible cubic polynomials can be generated by using the following two variable transformations: x=x + i, x=j−1x, i, j ∈ Fp, j ≠ 0. Based on the classification and that necessary fact, we show the number of the irreducible cubic polynomials in the form of x(3)+ax+b, b ∈ F(p), where a is a certain fixed element in F(p).
キーワード
Irreducible cubic polynomial
trace
quadratic residue
出版物タイトル
Memoirs of the Faculty of Engineering, Okayama University
発行日
2007-01
41巻
1号
出版者
Faculty of Engineering, Okayama University
出版者(別表記)
岡山大学工学部
開始ページ
1
終了ページ
10
ISSN
0475-0071
NCID
AA10699856
資料タイプ
紀要論文
OAI-PMH Set
岡山大学
言語
English
論文のバージョン
publisher
NAID
Eprints Journal Name
mfe