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3 Acta Arithmetica

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Sur les polynomes f(X,Y) tels que K[f] est integralement ferme dans K[X,Y]

100%

Ayad M.

tom 105

nr 1

9-28

Irreducibility of the iterates of a quadratic polynomial over a field

63%

Ayad M. , McQuillan D.

Acta Arithmetica

2000

tom 93

nr 1

87-97

1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define $f_{r+1}(X) = f(f_r(X))$ for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if $f_r(X)$ is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof. In the sequel we shall use elementary methods for proving the stability of quadratic polynomials over number fields; especially the rational field, and over finite fields of characteristic p ≥ 3.

Corrections to "Irreducibility of the iterates of a quadratic polynomial over a field" (Acta Arith. 93 (2000), 87-97)

63%

Ayad M. , McQuillan D.

Acta Arithmetica

2001

tom 99

nr 1