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On the Discriminants of the Powers of an Algebraic Integer
Part of:
Diophantine approximation, transcendental number theory
Algebraic number theory: global fields
Published online by Cambridge University Press: 22 May 2019
Abstract
For $\unicode[STIX]{x1D6FC}$ an algebraic integer of any degree $n\geqslant 2$, it is known that the discriminants of the orders $\mathbb{Z}[\unicode[STIX]{x1D6FC}^{k}]$ go to infinity as $k$ goes to infinity. We give a short proof of this result.
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