The class number one problem for some totally complex quartic number fields (Q1019833)
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scientific article; zbMATH DE number 5559083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The class number one problem for some totally complex quartic number fields |
scientific article; zbMATH DE number 5559083 |
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The class number one problem for some totally complex quartic number fields (English)
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28 May 2009
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Let \(K\) be a totally complex quartic field whose class number is equal to \(1\). The authors prove that there are 95 non-isomorphic fields \(K\) whose rings of algebraic integers are generated by an algebraic unit. Moreover, they prove Louboutin's conjecture according to which a totally complex quartic unit \(\varepsilon\) generally generates the unit group of the quartic order \(\mathbb Z[\varepsilon]\).
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quartic field
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fundamental unit
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class number
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