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On stable quadratic polynomials


Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E (2012). On stable quadratic polynomials. Glasgow Mathematical Journal, 54(2):359-369.

Abstract

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

Abstract

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

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Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Language:English
Date:1 May 2012
Deposited On:09 Nov 2018 19:19
Last Modified:24 Sep 2019 23:42
Publisher:Cambridge University Press
ISSN:0017-0895
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s001708951200002x
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S001708951200002X (Library Catalogue)

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