Grundlehren der mathematischen Wissenschaften

Perfect Lattices in Euclidean Spaces

Authors: Martinet, Jacques

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About this book

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.

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)


Table of contents (16 chapters)

Buy this book

eBook 84,99 €
price for Spain (gross)
  • ISBN 978-3-662-05167-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,95 €
price for Spain (gross)
  • ISBN 978-3-540-44236-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,95 €
price for Spain (gross)
  • ISBN 978-3-642-07921-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Perfect Lattices in Euclidean Spaces
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
327
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-05167-2
DOI
10.1007/978-3-662-05167-2
Hardcover ISBN
978-3-540-44236-3
Softcover ISBN
978-3-642-07921-4
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XXI, 526
Topics