Normal bases for rings of integers and modular units
type: Item
instance of: scholarly article
title: Normal bases for rings of integers and modular units
zbMATH Open document ID: 0806.11051
DOI: 10.1007/BF02567609
published in: Manuscripta Mathematica
publication date: 1994-08-10T00:00:00Z
full work available at URL: https://eudml.org/doc/155956
review text: Let \(K\) be an imaginary quadratic field with discriminant \(d_ K< -4\), \(d_ K\equiv 2,3\bmod 4\), and \(p\) a prime number, \(p\equiv 1\bmod 8\), \(p\) splits in \(K\). Furthermore, let \(\Omega_ p\) be the ring class field over \(K\) with conductor \(p\) and \(K(p)\) the ray class field over \(K\) with conductor \(p\). An explicit basis is constructed for the ring of integers of the unique quadratic extension of \(\Omega_ p\) contained in \(k(p)\) over the ring of integers of \(\Omega_ p\). This uses certain classical modular units considered by Deuring and Hecke.
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11G16
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 617426
zbMATH Keywords: normal integral basis
zbMATH Keywords: ring of integers
zbMATH Keywords: quadratic extension
zbMATH Keywords: modular units
author: Eugenio Jesús Gómez Ayala
reviewed by: J. Brinkhuis
MaRDI profile type: Publication
cites work: Q5532660
cites work: Q3758001
cites work: Q5735284
cites work: Arithmetic and Galois module structure for tame extensions.
cites work: Herleitung des Euler-Produktes der Zetafunktion und einiger \(L\)-Reihen aus ihrer Funktionalgleichung
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OpenAlex ID: W2081955286
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description: scientific article; zbMATH DE number 617426