Irreducibility of the iterates of a quadratic polynomial over a field
Acta Arithmetica, Tome 93 (2000) no. 1, pp. 87-97
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_aa_93_1_87_97,
author = {Mohamed Ayad and Donald McQuillan},
title = {Irreducibility of the iterates of a quadratic polynomial over a field},
journal = {Acta Arithmetica},
pages = {87--97},
year = {2000},
volume = {93},
number = {1},
doi = {10.4064/aa-93-1-87-97},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa-93-1-87-97/}
}
TY - JOUR AU - Mohamed Ayad AU - Donald McQuillan TI - Irreducibility of the iterates of a quadratic polynomial over a field JO - Acta Arithmetica PY - 2000 SP - 87 EP - 97 VL - 93 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/aa-93-1-87-97/ DO - 10.4064/aa-93-1-87-97 LA - en ID - 10_4064_aa_93_1_87_97 ER -
Mohamed Ayad; Donald McQuillan. Irreducibility of the iterates of a quadratic polynomial over a field. Acta Arithmetica, Tome 93 (2000) no. 1, pp. 87-97. doi: 10.4064/aa-93-1-87-97
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