Abstract
For an infinite family of real biquadratic fields k we give the structure of the Iwasawa module \(X=X(k_{\infty})\) of the \(\mathbb{Z}_{2}\)-extension of k. For these fields, we obtain that \(\lambda=\mu=0 \mbox{ and }\nu=2\). where \(\lambda\), \(\mu\) and \(\nu\) are the Iwasawa invariants of the cyclotomic \(\mathbb{Z}_{2}\)-extension of k
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El Mahi, A. On the structure of the Iwasawa module for \(\mathbb{Z}_{2}\)-extensions of certain real biquadratic fields. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01459-2
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DOI: https://doi.org/10.1007/s10474-024-01459-2
Key words and phrases
- Iwasawa theory
- \(\mathbb{Z}_{2}\)-extension
- real biquadratic field
- 2-class group
- class field theory
- unit