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Shells of selfdual lattices viewed as spherical designs

Claude Pache
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Abstract

We find out for which $t$ shells of selfdual lattices and of theirs shadows are spherical $t$-designs. The method uses theta series of lattices, which are modular forms. We analyse fully cubic and Witt lattices, as well as all selfdual lattices of rank at most 24.

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Claude Pache. 2005-02-15. Shells of selfdual lattices viewed as spherical designs. https://arxiv.org/abs/math/0502313

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