Juan Marcos Cerviño, Georg Hein
Published 2011-06-24Version 1
We study the theta map which assigns to a real quadratic form its theta series. We introduce two invariants reflecting whether the differential of the theta map vanishes or is degenerate. We provide examples of lattices where this differential is zero. These invariants turn out to be modular forms for integral lattices. We illustrate this in the rank two case.
Reduction mod $\ell$ of Theta Series of Level $\ell^n$
Cubic identities for theta series in three variables
General coefficient-vanishing results associated with theta series
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