Idoneal numbers and some generalizations
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 \(2\).
scientific article; zbMATH DE number 6039659