On the group of units of number fields of degree 2 and 4. (Sur le groupe des unités de corps de nombres de degré 2 et 4.) (French. English summary) Zbl 1196.11150

Ziane, M’hammed

J. Théor. Nombres Bordx. 19, No. 3, 799-808 (2007).

Summary: We give under certain hypotheses, a fundamental system of units of the field \(K=\mathbb Q(\omega)\) and its quadratic subfield, where \(\omega\) is a root of the polynomial \(f(X)=X^4 +d^{-2} M_6 X^2 -M_4\), with \(M_6 =D^6 +6D^4 d+9D^2 d^2 +2d^3\), \(M_4 =D^4 +4D^2 d+2d^2\), \(d, D\in\mathbb N\), \(d\mid D\).

MSC:

11R27	Units and factorization
11R11	Quadratic extensions
11R16	Cubic and quartic extensions
11R04	Algebraic numbers; rings of algebraic integers

Keywords:

fundamental system of units; number fields of degree 2 and 4

References:

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