On the Iwasawa invariants of the cyclotomic \(\mathbb Z_2\)-extensions of certain real quadratic fields (Q854388)
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scientific article; zbMATH DE number 5079811
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Iwasawa invariants of the cyclotomic \(\mathbb Z_2\)-extensions of certain real quadratic fields |
scientific article; zbMATH DE number 5079811 |
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On the Iwasawa invariants of the cyclotomic \(\mathbb Z_2\)-extensions of certain real quadratic fields (English)
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12 December 2006
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The author proves that the Iwasawa \(\lambda\)- and \(\mu\)-invariant of the cyclotomic \({\mathbb Z}_2\)-extension of \({\mathbb Q}(\sqrt m)\) and \({\mathbb Q}(\sqrt {2m})\) are zero, when \(m(>0)\) is a product of two primes satisfying certain conditions. The proof follows an idea by \textit{T. Fukuda} and \textit{K. Komatsu} who proved a similar result in [Tokyo J. Math. 28, No. 1, 259--264 (2005; Zbl 1080.11080)].
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Iwasawa theory
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quadratic extensions
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Abelian extensions
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class numbers
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