ON STABLE QUADRATIC POLYNOMIALS

被引：12

作者：

Ahmadi, Omran ^{[1
]}

Luca, Florian ^{[2
]}

Ostafe, Alina ^{[3
]}

Shparlinski, Igor E. ^{[4
]}

机构：

[1] Univ Coll Dublin, Claude Shannon Inst, Dublin 4, Ireland

[2] Univ Nacl Autonoma Mexico, Inst Math, Morelia 58089, Michoacan, Mexico

[3] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[4] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

来源：

GLASGOW MATHEMATICAL JOURNAL | 2012年 / 54卷 / 02期

基金：

爱尔兰科学基金会;

关键词：

BOUNDS;

D O I：

10.1017/S001708951200002X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We recall that a polynomial f (X) is an element of K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f (X) is an element of Z[X] are stable over Q. We also show that the presence of squares in so-called critical orbits of a quadratic polynomial f (X) is an element of Z[X] can be detected by a finite algorithm; this property is closely related to the stability of f (X). We also prove there are no stable quadratic polynomials over finite fields of characteristic 2 but they exist over some infinite fields of characteristic 2.

引用

页码：359 / 369

页数：11

共 17 条

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