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Book Review
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Book Information
Author(s):
Jacques Martinet
Title:
Perfect lattices in Euclidean spaces
Additional book information:
Springer-Verlag,
Berlin,
2003,
xxii + 523,
$99.00,
3-540-44236-7
References:
-
- 1.
- E.S. Barnes, The perfect and extreme senary forms. Canad. J. Math. 9 (1957), 235-242. MR 19:251e
- 2.
- A.-M. Bergé, J. Martinet, Sur un problème de dualité lié aux sphères en géométrie des nombres. J. Number Theory 32 (1989), no. 1, 14-42. MR 90g:11088
- 3.
- H.F. Blichfeldt, The minimum value of positive quadratic forms in six, seven, and eight variables. Math. Z. 39 (1935), 1-15.
- 4.
- H. Cohn, A. Kumar, The optimality of the Leech lattice. (preprint, 2003) available via: http://research.microsoft.com/
 cohn/Leech/ - 5.
- J.H. Conway, N.J.A. Sloane, Sphere packings, lattices and groups. Grundlehren 290, Springer (1988). MR 89a:11067
- 6.
- L.E. Dickson, History of the theory of numbers III, quadratic and higher forms. Chelsea, New York (1966). MR 39:6807c
- 7.
- W. Ebeling, Lattices and codes. Vieweg (1994). MR 95c:11084
- 8.
- N. Hofreiter, Über Extremformen. Monatshefte f. Math. 40 (1933), 129-152.
- 9.
- D.-O. Jaquet-Chiffelle, Énumération complète des classes de formes parfaites en dimension
 . Ann. Inst. Fourier (Grenoble) 43 (1993), no. 1, 21-55. MR 94d:11048 - 10.
- A. Korkine, G. Zolotareff, Sur les formes quadratiques. Math. Ann. 5 (1872) 581-583, ibid. 6 (1873) 366-389, ibid. 11 (1877) 242-292.
- 11.
- H. Minkowski, Geometrie der Zahlen. Teubner, Leipzig (1910).
- 12.
- J. Opgenorth, Dual cones and the Voronoi algorithm. Experiment. Math. 10 (2001), no. 4, 599-608. MR 2003c:11077
- 13.
- K.C. Stacey, The enumeration of perfect septenary forms. J. London Math. Soc. (2) 10 (1975), 97-104. MR 51:5507
- 14.
- B. B. Venkov, Réseaux et designs sphériques. Réseaux euclidiens, designs sphériques et formes modulaires, 10-86, Monogr. Enseign. Math. 37, Enseignement Math., Geneva (2001). MR 2002m:11061
- 15.
- G.F. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Journal f. d. Reine und Angewandte Mathematik 133 (1908), ibid. 134 (1908), ibid. 136 (1909).
Additional Information:
Reviewer(s):
Gabriele
Nebe
Affiliation:
Universität Ulm
Email:
nebe@mathematik.uni-ulm.de
Review Information:
Journal:
Bull. Amer. Math. Soc.
41
(2004),
529-533.
MSC
(2000):
Primary 11H31;
Secondary 11H55, 11H56, 11H71
DOI:
10.1090/S0273-0979-04-01018-3
PII:
S 0273-0979(04)01018-3
Posted:
March 24, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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