Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten
type: Item
instance of: scholarly article
title: Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten
zbMATH Open document ID: 0586.12008
DOI: 10.1007/BF01168487
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155123
review text: The author considers the quartic and octic residuacity properties of the fundamental unit \(\epsilon_ m\) of a quadratic field \({\mathbb{Q}}(\sqrt{m})\) modulo p in terms of the representability of p by quadratic forms. He comes up with ten criteria, which are too detailed to give here. The limitation is that there should not be too many components of order four in the construction of the ray class field modulo \(2^ s\) in \({\mathbb{Q}}(\sqrt{-m}).\) The author cites background material in his concurrent paper [J. Number Theory 22, 249-270 (1986; Zbl 0584.12005)]. He notes the direct generalization of results of \textit{E. Lehmer} [J. Reine Angew. Math. 268/269, 294-301 (1974; Zbl 0289.12007)] and the reviewer and \textit{G. Cooke} [Acta Arith. 30, 367-377 (1976; Zbl 0299.12004)].
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11A15
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 3939450
zbMATH Keywords: quartic residuacity
zbMATH Keywords: higher residuacity
zbMATH Keywords: binary quadratic forms
zbMATH Keywords: octic residuacity
zbMATH Keywords: fundamental unit
zbMATH Keywords: quadratic field
zbMATH Keywords: ray class field
author: Franz Halter-Koch
reviewed by: Harvey Cohn
MaRDI profile type: Publication
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OpenAlex ID: W2914437002
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description: scientific article; zbMATH DE number 3939450