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A dynamical characterization for monogenity at every level of some infinite
$2$-towers
Published online by Cambridge University Press: 20 October 2021
Abstract
We consider a concrete family of
$2$
-towers
$(\mathbb {Q}(x_n))_n$
of totally real algebraic numbers for which we prove that, for each
$n$
,
$\mathbb {Z}[x_n]$
is the ring of integers of
$\mathbb {Q}(x_n)$
if and only if the constant term of the minimal polynomial of
$x_n$
is square-free. We apply our characterization to produce new examples of monogenic number fields, which can be of arbitrary large degree under the ABC-Conjecture.
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- © Canadian Mathematical Society 2021
Footnotes
The work is part of my PhD thesis [1] under the supervision of X. Vidaux and C. R. Videla, to whom I am grateful for support and encouragement. It has been supported by the Conicyt fellowship “Beca Doctorado Nacional,” by the Universidad de Concepción (Chile), and by the Fondecyt research project 1130134 (Chile) of X. Vidaux. Part of this work was done while visiting Carlos R. Videla at Mount Royal University, Calgary, Canada. I am grateful to the referees for their careful reading of this paper, which helped improving the presentation and simplify some proofs.
References
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