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Zbl 1160.11334
Nebe, Gabriele
Lattices and modular forms. (Gitter und Modulformen.) (German)
[J] Jahresber. Dtsch. Math.-Ver. 104, No. 3, 125-144 (2002). ISSN 0012-0456

Summary: A main goal in lattice theory is the construction of dense lattices. Most of the remarkable dense lattices in small dimensions have an additional symmetry, they are modular, i.e. similar to their dual lattice. Extremal lattices are densest modular lattices, whose density is as high as the theory of modular forms allows it to be. The theory of theta series with harmonic coefficients allows to classify and to construct extremal lattices as well as to prove that some of them are strongly perfect and hence local maxima of the density function.

MSC 2000:: *11H31 Lattice packing and covering (number-theoretic results)
11-02 Research monographs (number theory)
11F11 Modular forms, one variable

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