Geometry of Numbers

C.G. Lekkerkerker, Pascale Gruber (Autoren)

Buch | Hardcover

731 Seiten

1987 | 2nd edition
North-Holland (Verlag)
978-0-444-70152-7 (ISBN)

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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.

Chapters: 1. Preliminaries. Supplement: Preliminaries. 2. Convex Bodies and Lattice Points. Supplement: Fundamental Theorems. Lattice Polytopes. Large Convex Bodies. Reduction Theory. Tiling. 3. The Critical Determinant, The Covering Constant and the Inhomogeneous Determinant of a Set. Supplement: Suprema and Infima over Lattices. Packing. Covering. 4. Star Bodies. Supplement: Boundary Lattice Points. 5. Some Methods. Note. 6. Homogeneous Forms. Supplement: Packing of Balls. Extreme Forms. Zeta-Functions. Homogeneous Minima. 7. Inhomogeneous Forms. Supplement: Covering with Balls. Product of Inhomogeneous Linear Forms. Inhomogeneous Forms. Geometry of Numbers in Other Spaces. References. Index.

Erscheint lt. Verlag	1.5.1987
Reihe/Serie	North-Holland Mathematical Library
Sprache	englisch
Gewicht	1110 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-444-70152-4 / 0444701524
ISBN-13	978-0-444-70152-7 / 9780444701527
Zustand	Neuware