Idoneal numbers and some generalizations (Q2888163)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Idoneal numbers and some generalizations |
scientific article; zbMATH DE number 6039659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Idoneal numbers and some generalizations |
scientific article; zbMATH DE number 6039659 |
Statements
30 May 2012
0 references
idoneal numbers
0 references
quadratic number fields
0 references
genus theory
0 references
elliptic curves
0 references
genus \(2\) curves
0 references
L-series
0 references
complex multiplication
0 references
0 references
Idoneal numbers and some generalizations (English)
0 references
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 \(2\).
0 references
