Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593931 | Journal of Number Theory | 2014 | 19 Pages |
Abstract
Suppose Q is a definite quadratic form on a vector space V over some totally real field K≠QK≠Q. Then the maximal integral ZKZK-lattices in (V,Q)(V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q)(V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 471 such genera. Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively. This classification also yields all maximal quaternion orders of type number one.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Markus Kirschmer,