Abstract
Let \(K= \mathbb {Q}(\sqrt{d})\) be a real quadratic field with d having three distinct prime factors. We show that the 2-class group of each layer in the \(\mathbb {Z}_2\)-extension of K is \(\mathbb {Z}/2\mathbb {Z}\) under certain elementary assumptions on the prime factors of d. In particular, it validates Greenberg’s conjecture on the vanishing of the Iwasawa \(\lambda \)-invariant for a new family of infinitely many real quadratic fields.
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Acknowledgements
The authors would like to sincerely thank the anonymous referee, whose valuable comments have helped in improving the manuscript. The authors also take immense pleasure to thank Indian Institute of Technology Guwahati for providing excellent facilities to carry out this research.
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Laxmi, H., Saikia, A. \(\mathbb {Z}_2\)-extension of real quadratic fields with \(\mathbb {Z}/2\mathbb {Z}\) as 2-class group at each layer. Ramanujan J (2024). https://doi.org/10.1007/s11139-024-00869-8
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DOI: https://doi.org/10.1007/s11139-024-00869-8