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The construction of unramified cyclic quartic extensions of \({\mathbb{Q}}(\sqrt{m})\). (English) Zbl 0576.12008
The author studies the dihedral field K for which K/\({\mathbb{Q}}(\sqrt{m})\) is unramified and cyclic of degree 4. Arithmetic conditions on m are given by analyzing the discriminant factors. [See the author’s earlier paper, Math. Comput. 40, 685-707 (1983; Zbl 0527.12006).] Illustrations include the cases \({\mathbb{Q}}(\sqrt{-14})\), \({\mathbb{Q}}(\sqrt{-46})\), etc., where K is the Hilbert class field.
Reviewer: Harvey Cohn
MSC:
11R23 Iwasawa theory
11R37 Class field theory
11R21 Other number fields
11R11 Quadratic extensions
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