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Book Review

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Book Information:

Author: Jacques Martinet
Title: Perfect lattices in Euclidean spaces
Additional book information: Springer-Verlag, Berlin, 2003, xxii + 523 pp., ISBN 3-540-44236-7, $99.00

References [Enhancements On Off] (What's this?)

  • 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 $7$. 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).

Review Information:

Reviewer: Gabriele Nebe
Affiliation: Universität Ulm
Email: nebe@mathematik.uni-ulm.de
Journal: Bull. Amer. Math. Soc. 41 (2004), 529-533
MSC (2000): Primary 11H31; Secondary 11H55, 11H56, 11H71
Published electronically: March 24, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society