Abstract
For an odd prime number $p$, we give an explicit upper bound of $\lambda$-invariants for all $\mathbb{Z}_p$-extensions of an imaginary quadratic field $k$ under several assumptions. We also give an explicit upper bound of $\lambda$-invariants for all $\mathbb{Z}_p$-extensions of $k$ in the case where the $\lambda$-invariant of the cyclotomic $\mathbb{Z}_p$-extension of $k$ is equal to 3.
Funding Statement
The author is partially supported by JSPS Core-to-core program, Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory.
Citation
Kazuaki MURAKAMI. "On an upper bound of $\lambda$-invariants of $\mathbb{Z}_p$-extensions over an imaginary quadratic field." J. Math. Soc. Japan 71 (3) 1005 - 1026, July, 2019. https://doi.org/10.2969/jmsj/77017701
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