## Journal of the Mathematical Society of Japan

### On an upper bound of $\lambda$-invariants of $\mathbb{Z}_p$-extensions over an imaginary quadratic field

Kazuaki MURAKAMI

#### 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.

#### Note

The author is partially supported by JSPS Core-to-core program, Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory.

#### Article information

Source
J. Math. Soc. Japan, Volume 71, Number 3 (2019), 1005-1026.

Dates
Revised: 2 April 2018
First available in Project Euclid: 25 April 2019

https://projecteuclid.org/euclid.jmsj/1556179397

Digital Object Identifier
doi:10.2969/jmsj/77017701

Mathematical Reviews number (MathSciNet)
MR3984250

Zentralblatt MATH identifier
07121561

Subjects
Primary: 11R23: Iwasawa theory

#### Citation

MURAKAMI, Kazuaki. On an upper bound of $\lambda$-invariants of $\mathbb{Z}_p$-extensions over an imaginary quadratic field. J. Math. Soc. Japan 71 (2019), no. 3, 1005--1026. doi:10.2969/jmsj/77017701. https://projecteuclid.org/euclid.jmsj/1556179397

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