ON STABLE QUADRATIC POLYNOMIALS
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 359-369
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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.
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
@article{10_1017_S001708951200002X,
author = {AHMADI, OMRAN and LUCA, FLORIAN and OSTAFE, ALINA and SHPARLINSKI, IGOR E.},
title = {ON {STABLE} {QUADRATIC} {POLYNOMIALS}},
journal = {Glasgow mathematical journal},
pages = {359--369},
year = {2012},
volume = {54},
number = {2},
doi = {10.1017/S001708951200002X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951200002X/}
}
TY - JOUR AU - AHMADI, OMRAN AU - LUCA, FLORIAN AU - OSTAFE, ALINA AU - SHPARLINSKI, IGOR E. TI - ON STABLE QUADRATIC POLYNOMIALS JO - Glasgow mathematical journal PY - 2012 SP - 359 EP - 369 VL - 54 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S001708951200002X/ DO - 10.1017/S001708951200002X ID - 10_1017_S001708951200002X ER -
%0 Journal Article %A AHMADI, OMRAN %A LUCA, FLORIAN %A OSTAFE, ALINA %A SHPARLINSKI, IGOR E. %T ON STABLE QUADRATIC POLYNOMIALS %J Glasgow mathematical journal %D 2012 %P 359-369 %V 54 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S001708951200002X/ %R 10.1017/S001708951200002X %F 10_1017_S001708951200002X
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