TY - JOUR
AB - 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.
AU - Kirschmer, Markus
ID - 42793
JF - Journal of Number Theory
KW - Algebra and Number Theory
SN - 0022-314X
TI - One-class genera of maximal integral quadratic forms
VL - 136
ER -