An elliptic resolvent
type: Item
instance of: scholarly article
title: An elliptic resolvent
zbMATH Open document ID: 0953.11034
author: Reinhard Schertz
published in: Journal of Number Theory
publication date: 2001-01-26T00:00:00Z
review text: The main subject of this paper is a generalization of previous results \textit{R. Schertz} [J. Number Theory 39, 285-326 (1991; Zbl 0739.11052)]. Let \(K\) be an imaginary quadratic number field and \({a}\), \( {b}\) integer ideals in \(K\). The author gives an explicit Galois generator for the ring of integers of the ray class field over \(K\), in relative extensions \(K( {qa})/K( {q})\) with some hypothesis on \( {q}\) and \( {a}\). Starting with new resolvent relations and an analytical interpretation for Galois extensions of fields of elliptic functions with respect to lattices \(\Gamma\subset\hat \Gamma\), he obtains the main result by using singular values of these functions in the complex multiplication context. Then the author applies his result to give explicit generators for Kummer orders considered in \textit{A. Srivastav} and \textit{M. J. Taylor} [Invent. Math. 99, 165-184 (1990; Zbl 0705.14031)].
reviewed by: Thong Nguyen Quang Do
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1309270
zbMATH Keywords: Galois module structure
zbMATH Keywords: explicit Galois generator
zbMATH Keywords: explicit generators for Kummer orders
MaRDI profile type: Publication
full work available at URL: jnth.1998.2369
OpenAlex ID: W1965492933
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DOI: 10.1006/JNTH.1998.2369
description: scientific article; zbMATH DE number 1309270