On Length Spectra of Lattices

• Tác giả: Thomas Willging
• Ngôn ngữ: eng
• ISBN-13: 978-3866445840
• ISBN: KSP/1000020381
• Ký hiệu phân loại: 512.12 Algebra and Euclidean geometry
• Thông tin xuất bản: Karlsruhe : KIT Scientific Publishing, 2010
• Mô tả vật lý: 1 electronic resource (55 p. p.)
• Bộ sưu tập: Tài liệu truy cập mở
• ID: 203562

Tóm tắt

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.