ON STABLE QUADRATIC POLYNOMIALS
2012 ◽
Vol 54
(2)
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pp. 359-369
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Keyword(s):
AbstractWe 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.
2013 ◽
Vol 24
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pp. 136-147
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2014 ◽
Vol 29
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pp. 118-131
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Keyword(s):
2015 ◽
Vol 24
(3)
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pp. 304-311
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2016 ◽
Vol 15
(07)
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pp. 1650133
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Keyword(s):
2001 ◽
Vol 21
(3)
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pp. 412-416
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