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

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).

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).

@article{JTNB_2005__17_3_905_0,
     author = {Michael E. Pohst and Marcus Wagner},
     title = {On the computation of Hermite-Humbert constants for real quadratic number fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {905--920},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {3},
     year = {2005},
     doi = {10.5802/jtnb.526},
     zbl = {05016593},
     mrnumber = {2212131},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.526/}
}
Michael E. Pohst; Marcus Wagner. On the computation of Hermite-Humbert constants for real quadratic number fields. Journal de Théorie des Nombres de Bordeaux, Tome 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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