Sur la construction d'un corps de Hilbert

We are concerned with the following: If k is a quadratic field and N a cyclic unramified extension of degree qⁿ over k, q a prime number, determine N explicitely via a primitive element , i.e., N=k(), in the spirit of Helmut Hasse 3]. We propose a method which determines these extensions, once we are able to specify the arithmetic of a certain field . To explicit our method, we construct the Hilbert fields of (226) and (646).