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Décomposition des nombres premièrs dans des extensions non abéliennes. (French) Zbl 0326.12005
Summary: Let \(K\) be a number field normal over \(\mathbb Q\) with Galois group \(G\) containing a normal abelian subgroup \(H\) with the following properties: \(H\) is of odd order if its fixed field is a real field of degree greater than 2 and the “Verlagerung” application associated with \(H\) is trivial. It is shown that the decomposition of a prime number in \(K\) depends on its representation by some forms with integral coefficients and with degree and number of variables equal to the index of \(H\) in \(G\).

MSC:
11R21 Other number fields
11E76 Forms of degree higher than two
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References:
[1] GAUSS, Arithmetishe untersuchungen, Werke Bd (traduction française : Blanchard ; traduction anglaise : Yale Univ. Press).
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