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Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$ , i.e., isomorphic to $ℤ / 2 ℤ \times ℤ / 2 ℤ \times ℤ / 2 ℤ$ . The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^{(*)}$ of $K$ .

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

1. Introduction. Let p be a prime number and $ℤ_{p}$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{\infty}$ a $ℤ_{p}$ -extension of k, $k_{n}$ the nth layer of $k_{\infty} / k$ , and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ . Iwasawa proved the following well-known theorem about the order $A_{n}$ of $A_{n}$ : Theorem A (Iwasawa). Let $k_{\infty} / k$ be a $ℤ_{p}$ -extension and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ , where $k_{n}$ is the $n$ th layer of $k_{\infty} / k$ . Then there exist integers $λ = λ (k_{\infty} / k) \geq 0$ , $μ = μ (k_{\infty} / k) \geq 0$ , $ν = ν (k_{\infty} / k)$ , and n₀ ≥ 0 such that $A_{n} = p^{λ n + μ p^{n} + ν}$ for...

On the vanishing of Iwasawa invariants of geometric cyclotomic ℤₚ-extensions

Akira Aiba (2003)

Acta Arithmetica

On the µ-invariants of cyclotomic fields

Kenkichi Iwasawa (1972)

Acta Arithmetica

Ordinary $p$ -adic Eisenstein series and $p$ -adic $L$ -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for ${GL}_{2} \times 𝒦^{\times}$ by the method of Eisenstein congruence on $G U (3, 1)$ , where $𝒦$ is an imaginary quadratic field. We construct a $p$ -adic family of ordinary Eisenstein series on the group of unitary similitudes $G U (3, 1)$ with the optimal constant term which is basically the product of the Kubota-Leopodlt $p$ -adic $L$ -function and a $p$ -adic $L$ -function for ${GL}_{2} \times 𝒦^{\times}$ . This construction also provides a different point of view of $p$ -adic...

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On the p-adic Leopoldt transform of a power series

On the parity of ranks of Selmer groups. III.

On the Pellian equation and the class number of indefinite binary quadratic forms.

On the power series attached to p-adic L-functions.

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

On the Stickelberger Ideal and the Circular Units of an Abelian Field.

On the structure of certain Galois cohomology groups.

On the structure of ideal class groups of CM-fields.

On the structure of the 2-Iwasawa module of some number fields of degree 16

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

On the vanishing of Iwasawa invariants of geometric cyclotomic ℤₚ-extensions

On the µ-invariants of cyclotomic fields

Ordinary $p$ -adic Eisenstein series and $p$ -adic $L$ -functions for unitary groups

$p$ -adic heights for semi-stable abelian varieties

$p$ -adic $L$ -functions for unitary Shimura varieties. I: Construction of the Eisenstein measure.

$p$ -adic representations arising from descent on abelian varieties

$p$ -adic representations of a local field. (Représentations $p$ -adiques d'un corps local.)

p-adic L-functions and p-adic periods of modular forms.

Parametric form of an eight class field

Petits discriminants

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