An application of Siegel’s formula over quaternion orders. (English) Zbl 0538.10027
This paper is concerned with Hermitian forms over a maximal order in a definite quaternion skew field H/\({\mathbb{Q}}\) such that the associated quadratic forms are positive definite and unimodular. An ad hoc proof of Siegel’s formula for the representation of numbers and an application to the existence of forms with large minimum are given. For \(H=(-1,-1)\) the forms are classified up to real dimension 24.
MSC:
11H55 | Quadratic forms (reduction theory, extreme forms, etc.) |
11E12 | Quadratic forms over global rings and fields |
11F11 | Holomorphic modular forms of integral weight |
11R52 | Quaternion and other division algebras: arithmetic, zeta functions |
Keywords:
extremal lattices; Hermitian forms; quaternion skew field; Siegel’s formula; forms with large minimumReferences:
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