Ramification and units of the cubic number field Q(zeta) generated by a root of x3+abx+B=0
J. R. Delgado (1987)
Extracta Mathematicae
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J. R. Delgado (1987)
Extracta Mathematicae
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H.C. Williams (1976)
Journal für die reine und angewandte Mathematik
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Francisca Cánovas Orvay (1991)
Extracta Mathematicae
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Franz Lemmermeyer, Attila Pethö (1995)
Manuscripta mathematica
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H. G. Grundman, L. L. Hall (2004)
Acta Arithmetica
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Jun Ho Lee, Stéphane R. Louboutin (2014)
Acta Arithmetica
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...
Isao Wakabayashi (2003)
Acta Arithmetica
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Hideo Yokoi (1974)
Journal für die reine und angewandte Mathematik
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Andrew Bremner (1989)
Manuscripta mathematica
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Robert F. Tichy, Volker Ziegler (2007)
Colloquium Mathematicae
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All purely cubic fields such that their maximal order is generated by its units are determined.
P. Pleasants (1966)
Acta Arithmetica
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Emery Thomas (1979)
Journal für die reine und angewandte Mathematik
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Gerhard Niklash (1997)
Collectanea Mathematica
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Haiyan Zhou (2006)
Acta Arithmetica
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Utz, W.R. (1982)
International Journal of Mathematics and Mathematical Sciences
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