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Séminaire de Théorie des Nombres

On the computation of Hermite-Humbert constants for real quadratic number fields

Marcus Wagner

( Berlin )

Salle de Conférences

le 15 décembre 2006 à 14:00

In 1965 Harvey Cohn presented an algorithm for the numerical approximation of low-points for the Hilbert modular group of real quadratic number fields KK with h(K)=1h(K)=1. It turns out that in fact the low-points correspond to extreme Humbert forms of real quadratic number fields. For extreme Humbert forms we use the theory of Vorono"i and Coulangeon for characterization. In this talk we combine the advantages of known algorithms and Cohn's algorithm to obtain new examples of extreme Humbert forms. We are able to compute extreme Humbert forms for the fields Q(7)Q(\sqrt{7}), Q(11)Q(\sqrt{11}) and Q(6)Q(\sqrt{6}).