Abstract

This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.
This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definite advantage of showing clearly where recent progress has taken place and in what areas interesting results may be expected in the future.
This new edition is an important contribution to the literature on the geometry of numbers, and deserves a place in every tertiary library.
The Australian Mathematics Teacher
This excellent book can be used as a reference book as well as an advanced introduction to geometry of numbers.
Zentralblatt für Mathematik