Abstract
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 β, i.e., N=k(β), 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\(k_{\bar \chi } \). To explicit our method, we construct the Hilbert fields of ℚ(√226) and ℚ(√646).
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Lbekkouri, A. Sur la construction d'un corps de Hilbert. Manuscripta Math 65, 257–273 (1989). https://doi.org/10.1007/BF01303036
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DOI: https://doi.org/10.1007/BF01303036