Sphere Packings, Lattices and Groups by John Horton Conway, Neil J. A. Sloane

Sphere Packings, Lattices and Groups



Download Sphere Packings, Lattices and Groups




Sphere Packings, Lattices and Groups John Horton Conway, Neil J. A. Sloane ebook
ISBN: 0387985859, 9780387985855
Publisher: Springer
Format: djvu
Page: 776


More neat applications of theta functions. Sphere Packings, Lattices and Groups (Grundlehren der Mathematischen Wissenschaften (Springer)). C is a group and {n + mi, for all n,m, in Z} is a subgroup and you take the quotient group .. €�The study of continuous families of lattice is not done,. Eisenstein lattices (or the more general theta lattices introduced in [1]) are of interest in the theory of modular forms, as their theta series is a modular form of weight for the full Hermitian modular group with respect to (cf. Property that unit balls around the lattice points touch, each one of them having exactly 196560 neighbors. Of interpenetrating sphere packings and one type of interpenetrating layers of spheres. Conway andSloane, Sphere Packings, Lattices and Groups, Springer, 1998. On page 328 of Ernst Witt's Collected Papers Ina Kersten recalls that Witt gave a colloquium talk on January 27, 1970 in Hamburg entitled "Gitter und Mathieu-Gruppen" (Lattices and Mathieu-groups). Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften). Sloane, Sphere Packings, Lattices and Groups, vol. The paper [2] contains a classification of the Eisenstein lattices for , , and . Buy Compendium of Continuous Lattices by G. Now one can see that a torus can be made into a group as follows: take the complex plane and set equal to zero all points which are linear integral combinations of two vectors with different directions, say 1 and i. The paper 'Notes on sphere packings' appeared in 1967 in the Canad. 290, Springer, New York, NY, USA, 3rd edition, 1999. All homogeneous sphere packings and all interpenetrating layers of spheres were derived that can be realized in the ten orthorhombic trivariant lattice complexes belonging to the space groups of crystal class mmm without mirror symmetry. Altogether, the lattice complexes with trigonal characteristic space group (with 0, 1, 2 or 3 degrees of freedom) give rise to 225 types of sphere packing.