Overview

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.

Full Product Details

Author:   Jacques Martinet
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2003
Volume:   327
Dimensions:   Width: 15.50cm , Height: 2.80cm , Length: 23.50cm
Weight:   0.837kg
ISBN:  

9783642079214

ISBN 10:   3642079210
Pages:   526
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Reviews

From the reviews: It is worth saying at the outset that Perfect lattices in Euclidean spaces is a state-of-the-art research monograph (with exercises) by one of the leading experts in this rapidly developing field ! . Martinet's book appears in the same Springer series as Conway and Sloane's epochal Sphere packings, lattices and groups and it will be similarly appreciated by researchers in this area as a carefully written, historically aware and authoritative companion volume focusing on local methods in lattice theory. (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)

From the reviews: It is worth saying at the outset that Perfect lattices in Euclidean spaces is a state-of-the-art research monograph (with exercises) by one of the leading experts in this rapidly developing field ... . Martinet,s book appears in the same Springer series as Conway and Sloane,s epochal Sphere packings, lattices and groups and it will be similarly appreciated by researchers in this area as a carefully written, historically aware and authoritative companion volume focusing on local methods in lattice theory. (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)

From the reviews: It is worth saying at the outset that Perfect lattices in Euclidean spaces is a state-of-the-art research monograph (with exercises) by one of the leading experts in this rapidly developing field ... . Martinet's book appears in the same Springer series as Conway and Sloane's epochal Sphere packings, lattices and groups and it will be similarly appreciated by researchers in this area as a carefully written, historically aware and authoritative companion volume focusing on local methods in lattice theory. (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)

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