On the Iwasawa λ-invariant of the cyclotomic ℤ2-extension of ℚ(pq) and the 2-part of the class number of ℚ(pq,2 + 2)-Reference-Cited by-同舟云学术

On the Iwasawa λ-invariant of the cyclotomic ℤ2-extension of ℚ(pq) and the 2-part of the class number of ℚ(pq,2 + 2)

Published:2020-10-05 Issue:04 Volume:17 Page:931-958
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kumakawa Naoki¹^ORCID

Affiliation:

1. Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Abstract

In this paper, we study the Iwasawa [Formula: see text]-invariant of the cyclotomic [Formula: see text]-extension of [Formula: see text], where [Formula: see text] are distinct odd prime numbers satisfying certain arithmetic conditions. Moreover, we obtain an upper bound of the [Formula: see text]-part of the class number of certain quartic number fields by calculating the Sinnott index explicitly.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042121500160

Reference17 articles.

1. Class Number Parity

2. The Iwasawa Invariant μ p Vanishes for Abelian Number Fields

3. On Zp-extensions of real quadratic fields

4. On the Iwasawa $\lambda$-Invariant of the Cyclotomic $\mathbf{Z}_2$-Extension of a Real Quadratic Field

5. The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields

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