Even positive definite unimodular quadratic forms over real quadratic fields. (English) Zbl 0708.11023

Hsia, J. S.

Rocky Mt. J. Math. 19, No. 3, 725-733 (1989).

The Siegel mass formula for positive definite, even unimodular lattices over the ring of integers in a real quadratic field is stated, and the classification of such lattices of low rank is discussed for \({\mathbb{Q}}(\sqrt{5})\) and \({\mathbb{Q}}(\sqrt{2})\). The author and D. C. Hung have completed the classification for rank 8 over \({\mathbb{Q}}(\sqrt{2})\) in a later paper [Math. Ann. 283, 367-374 (1989; Zbl 0643.10013)].

Reviewer: H.G.Quebbemann

MSC:

11E12	Quadratic forms over global rings and fields
11E41	Class numbers of quadratic and Hermitian forms

Keywords:

Siegel mass formula; positive definite, even unimodular lattices; real quadratic field