Unit Groups and Class Numbers of Real Cyclic Octic Fields

DOI10.2307/2001860zbMath0738.11055OpenAlexW4246928646MaRDI QIDQ3979968

Yuanyuan Shen

Publication date: 26 June 1992

Full work available at URL: https://doi.org/10.2307/2001860

zbMATH Keywords

class numberregulatorfundamental unitsunit groupreal cyclic octic fieldssimplest octic fields

Mathematics Subject Classification ID

Units and factorization (11R27) Other number fields (11R21) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Polynomials (irreducibility, etc.) (11R09)

Related Items (7)

Fundamental units in a parametric family of not totally real quintic number fields ⋮ Automatic solution of families of Thue equations and an example of degree 8 ⋮ Complete solutions to a family of Thue equations of degree 12 ⋮ HT90 and ``simplest number fields ⋮ Dihedral and cyclic extensions with large class numbers ⋮ NUMBER OF SQUFNITS IN A BIQUADRATIC FIELD ⋮ Noether's problem and $\mathbb{Q}$-generic polynomials for the normalizer of the $8$-cycle in $S_8$ and its subgroups

Cites Work

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• An inequality relating the regulator and the discriminant of a number field
• Class numbers of cyclotomic fields
• The Simplest Cubic Fields
• Special Units in Real Cyclic Sextic Fields
• Class Number Computations of Real Abelian Number Fields
• Number fields

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