@article{42793,
abstract = {{Suppose Q is a definite quadratic form on a vector space V over some totally real field K ≠ 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 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.}},
author = {{Kirschmer, Markus}},
issn = {{0022-314X}},
journal = {{Journal of Number Theory}},
keywords = {{Algebra and Number Theory}},
pages = {{375--393}},
publisher = {{Elsevier BV}},
title = {{{One-class genera of maximal integral quadratic forms}}},
doi = {{10.1016/j.jnt.2013.10.007}},
volume = {{136}},
year = {{2014}},
}