On Length Spectra of Lattices
Abstract
The aim of this work is to study Schmutz Schaller's conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume. Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.
Keywords
Lattices; Geodesics; Quadratic FormsISBN
9783866445840Publisher
KIT Scientific PublishingPublisher website
http://www.ksp.kit.edu/Publication date and place
2010Classification
Mathematics & science