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ISSN 1088-9485(e) ISSN 0273-0979(p)

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 pp., $99.00, ISBN 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/ $\sim$ 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
PII: S 0273-0979(04)01018-3
Posted: March 24, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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