One very simple version of the theta function is as a generating function over the perfect squares:
$$ \theta(\tau; z) = \sum_{n\in \mathbb{Z}} q^{n^2} w^{2n} $$
Where $q = e^{2\pi i \tau}$ and $w = e^{\pi i z}$. I want to know what is the "meaning" or series-expansion of the reciprocal of the theta function:
$$ \frac{1}{\theta(q,w)} = \sum_{n\in \mathbb{Z}} (\dots)q^n $$
This is the kind of things I might run through a computer, I still have no idea what the coefficients should mean.
Not sure if it leads anywhere, but an idea might be to use Jacobi triple product, write each factor as a q-Pochhammer symbol and use the formula on the wikipedia for the inverse of such symbols to try and come up with a physical interpretation...