We give an improvement of a result of J. Martinet on Stickelbergers 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.
Revised:
Published online:
DOI: 10.5802/jtnb.723
Classification: 11R29, 11R37
Keywords: Number fields, Discriminants, Stickelberger congruences, Class field theory, Kummer theory
Author's affiliations:
@article{JTNB_2010__22_2_397_0, author = {Georges Gras}, title = {Stickelberger{\textquoteright}s congruences for absolute norms of relative discriminants}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {397--402}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {2}, year = {2010}, doi = {10.5802/jtnb.723}, mrnumber = {2769070}, zbl = {1239.11124}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.723/} }
TY - JOUR TI - Stickelberger’s congruences for absolute norms of relative discriminants JO - Journal de Théorie des Nombres de Bordeaux PY - 2010 DA - 2010/// SP - 397 EP - 402 VL - 22 IS - 2 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.723/ UR - https://www.ams.org/mathscinet-getitem?mr=2769070 UR - https://zbmath.org/?q=an%3A1239.11124 UR - https://doi.org/10.5802/jtnb.723 DO - 10.5802/jtnb.723 LA - en ID - JTNB_2010__22_2_397_0 ER -
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 -primary units. Jour. de Théorie des Nombres de Bordeaux 21 (2009), 733–740. | Numdam | Zbl: pre05774808
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