On the computation of Hermite-Humbert constants for real quadratic number fields
Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 905-920.

We present algorithms for the computation of extreme binary Humbert forms in real quadratic number fields. With these algorithms we are able to compute extreme Humbert forms for the number fields (13) and (17). Finally we compute the Hermite-Humbert constant for the number field (13).

Nous présentons des algorithmes pour le calcul des formes de Humbert binaires extrémales sur les corps quadratiques réels. Grâce à ces algorithmes, nous sommes capables de calculer les formes de Humbert extrémales pour les corps de nombres (13) et (17). Enfin nous calculons la constante d’Hermite-Humbert pour le corps de nombres (13).

Published online:
DOI: 10.5802/jtnb.526
Michael E. Pohst 1; Marcus Wagner 1

1 Technische Universität Berlin Fakultät II Institut für Mathematik MA 8-1 Str. d. 17. Juni 136 D-10623 Berlin, Germany
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Michael E. Pohst; Marcus Wagner. On the computation of Hermite-Humbert constants for real quadratic number fields. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 905-920. doi : 10.5802/jtnb.526. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.526/

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