Abstract
The Hermite constant $\gamma_n(D)$ of a quaternion skew field $D$ over a global field is defined and studied. We obtain an upper bound of $\gamma_{n}(D)$. In the case that the base field is a number field, we introduce the notion of quaternionic Humbert forms over $D$. Then $\gamma_{n}(D)$ is characterized as a critical value of the Hermite invariants for $n$-ary quaternionic Humbert forms. We extend Voronoï's theorem on extreme forms to quaternionic Humbert forms.
Citation
Renaud Coulangeon. Takao Watanabe. "Hermite constant and Voronoï theory over a quaternion skew field." Osaka J. Math. 43 (3) 517 - 556, September 2006.
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