One-class genera of maximal integral quadratic forms
Kirschmer, Markus
Algebra and Number Theory
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.
Elsevier BV
2014
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/42793
Kirschmer M. One-class genera of maximal integral quadratic forms. <i>Journal of Number Theory</i>. 2014;136:375-393. doi:<a href="https://doi.org/10.1016/j.jnt.2013.10.007">10.1016/j.jnt.2013.10.007</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2013.10.007
info:eu-repo/semantics/altIdentifier/issn/0022-314X
info:eu-repo/semantics/closedAccess