Skip to main content Accessibility help
×
Home

On the Discriminants of the Powers of an Algebraic Integer

  • Stéphane R. Louboutin (a1)

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.

Copyright

References

Hide All
[Dub] Dubickas, A., On the discriminant of the power of an algebraic number . Stud. Sci. Math. Hungar. 44(2007), 2734. https://doi.org/10.1556/SScMath.2006.1001
[EG] Evertse, J.-H. and Györy, K., Discriminant equations in Diophantine number theory . New Math. Monogr., 32, Cambridge University Press, Cambridge, 2017. https://doi.org/10.1017/CBO9781316160763
[Gross] Grossman, E. H., Units and discriminants of algebraic number fields . Comm. Pure Appl. Math. 27(1974), 741747. https://doi.org/10.1002/cpa.3160270603
[Lou10] Louboutin, S., On some cubic or quartic algebraic units . J. Number Theory 130(2010), 956960. https://doi.org/10.1016/j.jnt.2009.09.002
[Lou12] Louboutin, S., On the fundamental units of a totally real cubic order generated by a unit . Proc. Amer. Math. Soc. 140(2012), 429436. https://doi.org/10.1090/S0002-9939-2011-10924-9
[Lou15] Louboutin, S., Fundamental units for some orders generated by a unit . In: Publ. Math. Besançon Algèbre et Théorie des Nombres , Presses Univ. Franche-Comté, Besançon, 2015, pp. 4168.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

On the Discriminants of the Powers of an Algebraic Integer

  • Stéphane R. Louboutin (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed