One-class genera of maximal integral quadratic forms

JOURNAL OF NUMBER THEORY

卷:136

Article

Kirschmer, Markus

关键词: Lattices;    Quadratic forms;    Class numbers;   

DOI  :  10.1016/j.jnt.2013.10.007

来源: Elsevier

【 摘 要 】

Suppose Q is a definite quadratic form on a vector space V over some totally real field K not equal Q. Then the maximal integral Z(K)-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 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free