The class number one problem for the real quadratic fields \(\mathbb {Q}(\sqrt {(an)^2+4a})\) (Q2787077)
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scientific article; zbMATH DE number 6545343
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The class number one problem for the real quadratic fields \(\mathbb {Q}(\sqrt {(an)^2+4a})\) |
scientific article; zbMATH DE number 6545343 |
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24 February 2016
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class number problem
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real quadratic field
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0.97813594
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0.9594588
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0.95248556
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0.94559366
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0.9414546
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0.93695825
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0.9295426
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The class number one problem for the real quadratic fields \(\mathbb {Q}(\sqrt {(an)^2+4a})\) (English)
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In [Acta Arith. 106, No. 1, 85--104 (2003; Zbl 1154.11338)], \textit{A. Biró} introduced a completely new method for solving the class number one problem in some families of real quadratic number fields. In this paper, using this method, the authors manage to solve the class number one problem for the family of real quadratic number fields of Richaud-Degert type \(\mathbb{Q}(\sqrt{d})\), where \(d=(an)^2+4a\) such that \(a\), \(n\) are odd positive integers and \((an)^2+4a\) is square-free.
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