Stickelberger’s congruences for absolute norms of relative discriminants
Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 397-402.

We give an improvement of a result of J. Martinet on Stickelberger s congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field theory.

Nous généralisons un résultat de J. Martinet sur les congruences de Stickelberger pour les normes absolues des discriminants relatifs des corps de nombres, en utilisant des arguments classiques du corps de classes.

Received:
Revised:
Published online:
DOI: 10.5802/jtnb.723
Classification: 11R29,  11R37
Keywords: Number fields, Discriminants, Stickelberger congruences, Class field theory, Kummer theory
Georges Gras 1

1 Villa la Gardette chemin Château Gagnière F-38520 Le Bourg d’Oisans
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Georges Gras. Stickelberger’s congruences for absolute norms of relative discriminants. Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 397-402. doi : 10.5802/jtnb.723. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.723/

[Gr] G. Gras, Class Field Theory: from theory to practice. SMM, Springer-Verlag, 2003; second corrected printing: 2005. | Zbl: 1019.11032

[Ma] J. Martinet, Les discriminants quadratiques et la congruence de Stickelberger. Sém. Théorie des Nombres, Bordeaux 1 (1989), 197–204. | Numdam | Zbl: 0731.11061

[Pi] S. Pisolkar, Absolute norms of p-primary units. Jour. de Théorie des Nombres de Bordeaux 21 (2009), 733–740. | Numdam | Zbl: pre05774808

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