Shells of selfdual lattices viewed as spherical designs

Claude Pache (1)

1 Section de mathématiques [Genève]

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.

Domaines: Combinatoire [math.CO]

Claude Pache. Shells of selfdual lattices viewed as spherical designs. 2005. ⟨hal-00004264⟩