One-class genera of maximal integral quadratic forms
نویسنده
چکیده
Suppose Q is a definite quadratic form on a vector space V over some totally real field K 6= Q. Then the maximal integral ZK-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (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 469 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.
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