Geodesic
ON STABLE QUADRATIC POLYNOMIALS
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 359-369

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S001708951200002X
Mots-clés : 11C08, 11T06, 37P05 
AHMADI, OMRAN; LUCA, FLORIAN; OSTAFE, ALINA; SHPARLINSKI, IGOR E. ON STABLE QUADRATIC POLYNOMIALS. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 359-369. doi: 10.1017/S001708951200002X
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