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
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
收藏
页码:359 / 369
页数:11
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