Gitter und Modulformen

Details Gitter und Modulformen Gitter und Modulformen

2002-11-15

arxiv.org/abs/math/0211233v1

DMV Jahresbericht, 104 (3), (2002) 123-142

Mathematics

Number Theory

Survey article

Scientific paper

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, whoses 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.

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