Some reults on fundamental units in cubic fields.
H.C. Williams (1976)
Journal für die reine und angewandte Mathematik
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H.C. Williams (1976)
Journal für die reine und angewandte Mathematik
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Hiroshi Yamashita (1993)
Manuscripta mathematica
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Jae Moon Kim, Seung Ik Oh (2000)
Acta Arithmetica
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Francisca Cánovas Orvay (1991)
Extracta Mathematicae
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Emery Thomas (1979)
Journal für die reine und angewandte Mathematik
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Franz Lemmermeyer, Attila Pethö (1995)
Manuscripta mathematica
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A. Popescu, N. Popescu, M. Vajaitu, A. Zaharescu (2002)
Acta Arithmetica
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Haiyan Zhou (2006)
Acta Arithmetica
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Shu-Leung Tang (1993)
Manuscripta mathematica
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Akira Aiba (2003)
Acta Arithmetica
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Scarowsky, Manny, Boyarsky, Abraham (1986)
International Journal of Mathematics and Mathematical Sciences
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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.
Masato Kurihara (2005)
Acta Arithmetica
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A.R. Wadsworth, P. Mammone, R. Moresi (1991)
Mathematische Zeitschrift
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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...
Tsuneo Arakawa (1982)
Mathematische Annalen
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