Idoneal numbers and some generalizations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1253.11049
author: Ernst Kani
publication date: 2012-05-30T00:00:00Z
full work available at URL: 35-2.html
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 11G30
zbMATH DE Number: 6039659
zbMATH Keywords: idoneal numbers
zbMATH Keywords: quadratic number fields
zbMATH Keywords: genus theory
zbMATH Keywords: elliptic curves
zbMATH Keywords: genus \(2\) curves
zbMATH Keywords: L-series
zbMATH Keywords: complex multiplication
MaRDI profile type: Publication
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title: Idoneal numbers and some generalizations
published in: Annales des Sciences Mathématiques du Québec
review text: Euler's idoneal numbers have been discussed in many articles and books, and most often, so it seems, with a substantial amount of inaccuracies (see e.g. \textit{F. Grube} [Schlömilch Z. (Z. Math. Phys.) 19, 492--519 (1874; JFM 06.0124.02)]). The first part of this very clearly written survey addresses a few more errors that have crept into various presentations, and lists the main properties of idoneal numbers. In addition, the connection between idoneal numbers, \(L\)-series, and complex multiplication is explained. The last part of this survey presents the author's discovery of a connection between idoneal numbers and the arithmetic of certain curves of genus \(2\).
reviewed by: Franz Lemmermeyer
description: scientific article; zbMATH DE number 6039659