Parametrization of the quadratic fields whose class numbers are divisible by three (Q1971701)
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scientific article; zbMATH DE number 1423156
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Parametrization of the quadratic fields whose class numbers are divisible by three |
scientific article; zbMATH DE number 1423156 |
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Parametrization of the quadratic fields whose class numbers are divisible by three (English)
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9 January 2002
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The authors show that every quadratic number field \(K\) with class number divisible by \(3\) has the form \(K = \mathbb Q(\sqrt{4uw^3 - 27u^2})\), where \(u, w\) are integers satisfying certain congruence conditions modulo \(27\). This result contains many previous constructions e.g. by \textit{P. Hartung} [J. Number Theory 6, 279-281 (1974; Zbl 0317.12002)], \textit{K. Ohta} [Mem. Gifu Tech. Coll. 17, 51-54 (1981)] and \textit{J. Brinkhuis} [Acta Arith. 69, 1-9 (1995; Zbl 0838.11073)] as special cases.
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quadratic number fields
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class number divisibility
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Hilbert class field
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