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Perfect lattices in Euclidean spaces. (English) Zbl 1017.11031
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.

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.)
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