On the capitulation in the genus field of an abelian extension of an imaginary quadratic field
type: Item
instance of: scholarly article
title: On the capitulation in the genus field of an abelian extension of an imaginary quadratic field
zbMATH Open document ID: 1081.11514
published in: Journal of Number Theory
publication date: 2001-01-01T00:00:00Z
review text: The aim of this note is to generalize the Principal Ideal Theorem to the genus field of an abelian extension of a quadratic imaginary field \(k\). We use the complex multiplication theory to find explicit generators for ambiguous ideals in the genus field of some abelian extensions of \(k\).
Mathematics Subject Classification ID: 11R37
zbMATH DE Number: 1547376
author: Caroline Thiébaud
MaRDI profile type: Publication
full work available at URL: jnth.2000.2550
OpenAlex ID: W2020459661
cites work: Principal ideal theorems in the genus field for absolutely abelian extensions
cites work: Konstruktion von Potenzganzheitsbasen in Strahlklassenkörpern über imaginär-quadratischen Zahlkörpern.
cites work: Q913858
cites work: An elliptic resolvent
cites work: Q3953865
cites work: Some applications of Kronecker's limit formulas
DOI: 10.1006/JNTH.2000.2550
description: scientific article; zbMATH DE number 1547376