On ideal class groups and units in terms of the quadratic form \(x^2+32y^2\) (Q2483727)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On ideal class groups and units in terms of the quadratic form \(x^2+32y^2\) |
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On ideal class groups and units in terms of the quadratic form \(x^2+32y^2\) (English)
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26 July 2005
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The authors investigate the narrow \(2\)-class group and the norm of the fundamental unit of quadratic number fields \(\mathbb Q (\sqrt{2p_1 \cdot\ldots\cdot p_{t-1}})\) with primes \(p_j \equiv 1 \negmedspace\mod 8\); mainly if the \(4\)-rank equals \(1\). The criteria (including density results) generalize the well-known results for \(t = 2\). The number of primes \(p_j\) which are of the form \(x^2 + 32y^2\) play a crucial role in the investigations.
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