2024 A weak form of Greenberg's conjecture for the cyclotomic $\mathbb{Z}_2$-extension of real quadratic fields
Naoki Kumakawa
Funct. Approx. Comment. Math. Advance Publication 1-13 (2024). DOI: 10.7169/facm/240331-2-9

Abstract

In this paper, we show that a weak form of Greenberg's conjecture for the cyclotomic $\mathbb{Z}_{2}$-extension of $\mathbb{Q}(\sqrt{p})$ is true, where $p$ is an odd prime number satisfying certain arithmetic conditions. As an application, we obtain an upper bound of the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_{2}$-extension of $\mathbb{Q}(\sqrt{p})$ under some additional conditions on $\mathbb{Q}(\sqrt{p})$.

Citation

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Naoki Kumakawa. "A weak form of Greenberg's conjecture for the cyclotomic $\mathbb{Z}_2$-extension of real quadratic fields." Funct. Approx. Comment. Math. Advance Publication 1 - 13, 2024. https://doi.org/10.7169/facm/240331-2-9

Information

Published: 2024
First available in Project Euclid: 16 December 2024

Digital Object Identifier: 10.7169/facm/240331-2-9

Subjects:
Primary: 11R11 , 11R29

Keywords: class numbers , Iwasawa invariants , quadratic fields

Rights: Copyright © 2024 Adam Mickiewicz University

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