Shells of selfdual lattices viewed as spherical designs

Mathematics – Combinatorics

Scientific paper

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Scientific paper

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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