Abstract
This is a continuation of my previous papers [2], [3], [4] concerning to the monstrous moonshine.The automorphism group ·O of the Leech lattice L plays an important role in the study of moonshine. Especially it is important to study theta functions associated with quadratic sublattices of L consisting of fixed vectors of elements of ·O. In this paper, we discuss the properties that these functions are expected to satisfy in the relation to the monstrous moonshine.
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