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Racines cubiques de nombres entiers et multiplication complexe dans les fonctions elliptiques

D. Mirimanoff (1903)

Mathematische Annalen

Relations between polynomial roots

Michael Drmota, Mariusz Skałba (1995)

Acta Arithmetica

Relations between polynomial roots

Michael Drmota, Mariusz Skałba (1995)

Acta Arithmetica

Relative Galois module structure of integers of abelian fields

Nigel P. Byott, Günter Lettl (1996)

Journal de théorie des nombres de Bordeaux

Let $L / K$ be an extension of algebraic number fields, where $L$ is abelian over $ℚ$ . In this paper we give an explicit description of the associated order $𝒜_{L / K}$ of this extension when $K$ is a cyclotomic field, and prove that $o_{L}$ , the ring of integers of $L$ , is then isomorphic to $𝒜_{L / K}$ . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that $𝒜_{L / K}$ is the maximal order if $L / K$ is a cyclic and totally wildly ramified extension which is linearly disjoint to $ℚ^{(m^{'})} / K$ , where $m^{'}$ is the conductor of $K$ .

Relative norms of units and 4-rank of class groups

Tommy Bülow (2005)

Acta Arithmetica

Remark on the minimum discriminant of normal fields

Juraj Kostra (1989)

Czechoslovak Mathematical Journal

Remarks on Unit indices of imaginary abelian number fields.

Mikihito Hirabayashi, Ken-ichi Yoshino (1988)

Manuscripta mathematica

Remarks on unit indices of imaginary abelian number fields II.

Mikihito Hirabayashi, Ken-ichi Yoshino (1989)

Manuscripta mathematica

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