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July, 2019 On an upper bound of $\lambda$-invariants of $\mathbb{Z}_p$-extensions over an imaginary quadratic field
Kazuaki MURAKAMI
J. Math. Soc. Japan 71(3): 1005-1026 (July, 2019). DOI: 10.2969/jmsj/77017701

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

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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

Information

Received: 27 December 2016; Revised: 2 April 2018; Published: July, 2019
First available in Project Euclid: 25 April 2019

zbMATH: 07121561
MathSciNet: MR3984250
Digital Object Identifier: 10.2969/jmsj/77017701

Subjects:
Primary: 11R23
Secondary: 11R11

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 3 • July, 2019
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