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Book Review
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Book Information
Author(s):
J. H. Conway and N. J. A. Sloane
Title:
Sphere packings, lattices and groups\/}, second ed.
Additional book information:
Grundlehren der Mathematischen Wissenschaften, bd. 290, Springer-Verlag, New York and Berlin, 1993, xliii+679 pp., US$69.00. ISBN 0-387-97912-3 and ISBN 3-540-97912-3
References:
- [1]
- H. F. Blichfeldt, A new principle in the geometry of numbers, Trans. Amer. Math. Soc. \textbf{15} (1914), 227--235.
- [2]
- J. W. S. Cassels, An introduction to the geometry of numbers, Springer-Verlag, New York, 1971.
- [3]
- H. S. M. Coxeter, L. Few, and C. A. Rogers, Covering space with equal spheres, Mathematika \textbf{6} (1959), 147--157.
- [4]
- L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und in Raum, Grundlehren Math. Wiss., bd. 65, Springer, Berlin, 1953.
- [5]
- L. Fejes Toth, Regular figures, Pergamon, Oxford, 1964.
- [6]
- L. Fejes Toth, On the densest packing of convex discs, Mathematika \textbf{30} (1983), 1--3.
- [7]
- P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers, 2nd ed., North-Holland, Amsterdam, 1987.
- [8]
- E. Hlawka, Zur Geometrie der Zahlen, Math. Z. \textbf{49} (1944), 285--312.
- [9]
- G. A. Kabatiansky and V. I. Levenshtein, Bounds for packings on a sphere and in space, Problems of Information Transmission \textbf{14} (1978), 1--17.
- [10]
- J. Kepler, The six-cornered snowflake, Translated from the Latin booklet of 1611 by Colin Hardie, Clarendon Press, Oxford, 1966.
- [11]
- H. Minkowski, Diphantische approximationen, Teubner, Leipzig, 1907.
- [12]
- H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910.
- [13]
- H. Minkowski, Gesammelte abhandlungen, Teubner, Berlin, 1911.
- [14]
- C. A. Rogers, Existence theorems in the geometry of numbers, Ann. of Math. (2) \textbf{48} (1947), 994--1002.
- [15]
- C. A. Rogers, Packing and covering, Cambridge Univ. Press, London and New York, 1964.
- [16]
- C. L. Siegel, A mean value theorem in the geometry of numbers, Ann. of Math. (2) \textbf{46} (1945), 340--347.
Additional Information:
Reviewer(s):
C. A.
Rogers
Review Information:
Journal:
Bull. Amer. Math. Soc.
29
(1993),
306-314.
DOI:
10.1090/S0273-0979-1993-00435-X
PII:
S 0273-0979(1993)00435-X
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