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Title: On stable quadratic polynomials
Related: Glasgow mathematical journal, Vol. 54, Issue 2, (2012), p.359-369
DOI: 10.1017/S001708951200002X
Publisher: Cambridge University Press
Date: 2012
Author/Creator: Ahmadi, Omran
Author/Creator: Luca, Florian
Author/Creator: Ostafe, Alina
Author/Creator: Shparlinski, Igor E
Description: We recall that a polynomial f(X)= 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) = 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) = 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.
Description: 11 page(s)
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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