Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten (Q1071807)

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)].