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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 \(G\).

11R21 Other number fields
11E76 Forms of degree higher than two
Full Text: DOI Numdam EuDML
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