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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

Stéphane R. Louboutin
Stéphane R. Louboutin*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France Email: stephane.louboutin@univ-amu.fr
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Abstract

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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.

Keywords

discriminantalgebraic integer

MSC classification

Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11R29: Class numbers, class groups, discriminants 11J86: Linear forms in logarithms; Baker's method
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 481 - 483
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Copyright
© Canadian Mathematical Society 2019

References

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