| 书目名称 | Perfect Lattices in Euclidean Spaces | | 编辑 | Jacques Martinet | | 视频video | | | 概述 | Long-awaited authoritative reference on this beautiful subject at the interface of geometry, number theory, coding theory and group theory.Complement to J.H. Conway and N.J.A. Sloane "Sphere Packings, | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | .Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3...This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property...Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290...Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.. | | 出版日期 | Book 2003 | | 关键词 | Euclidean lattices; Symbol; coding theory; eutactic lattices; number theory; perfect lattices; sphere pack | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-05167-2 | | isbn_softcover | 978-3-642-07921-4 | | isbn_ebook | 978-3-662-05167-2Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 2003 |
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发表于 2025-3-21 18:07:48
