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

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

Sphere packings, lattices and groups. Sloane, Sphere Packings, Lattices and Groups, vol. 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. (For more, of course, consult the excellent Sphere Packings, Lattices, and Groups from Conway and Sloane). Of interpenetrating sphere packings and one type of interpenetrating layers of spheres. More neat applications of theta functions. I have been working with issues somewhat tangential to the monster group, and more with the modular forms which are related to the lattice or sphere packing of E_8 and the Leech lattice ?_{24}. 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. Today I found myself reading the preface to the classic Conway-Sloane monograph Sphere Packings, Lattices and Groups. €�The study of continuous families of lattice is not done,. C is a group and {n + mi, for all n,m, in Z} is a subgroup and you take the quotient group .. Conway andSloane, Sphere Packings, Lattices and Groups, Springer, 1998. The paper [2] contains a classification of the Eisenstein lattices for , , and . Buy Compendium of Continuous Lattices by G. Yesterday I Googled trying to find some of the material in that book, but found nothing on-line. 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. 290, Springer, New York, NY, USA, 3rd edition, 1999. Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften).