Perfect lattices in Euclidean spaces. (English) Zbl 1017.11031

Martinet, Jacques

Grundlehren der Mathematischen Wissenschaften. 327. Berlin: Springer. xxi, 523 p. EUR 89.95/net; sFr 149.50; £63.00; $ 99.00 (2003).

The original French edition of the book was published in 1996 (see Zbl 0869.11056); this English edition is an improved and expanded version. Some sections have been completely rewritten, and the bibliography has been updated. A new appendix briefly reports on an interesting recent development (largely due to B. B. Venkov) that connects extreme lattices, spherical designs and modular forms.

Reviewer: Heinz Georg Quebbemann (Oldenburg)

MSC:

11H31	Lattice packing and covering (number-theoretic aspects)
11-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
52-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry
11H55	Quadratic forms (reduction theory, extreme forms, etc.)

Keywords:

perfect lattice; eutactic lattice; extreme lattice; Voronoi algorithm; sphere packing; density

Citations:

Zbl 0869.11056