I'm wondering about the general solution to the zeroes of polynomials via theta constants, as I came across it the other day on wikipedia. The notation for the theta constants didn't seem too elusive, until I looked them up and realized that there must be multiple conventions for the notation of these things. My question comes in two parts:
What does the general solution (or construction) to polynomial roots look like in theta constants and what is the best source material for these objects?
Here is the wiki for theta constants: https://en.wikipedia.org/wiki/Theta_constant. And here's the wiki for the general solution: https://en.wikipedia.org/wiki/Thomae%27s_formula.
This leads to another confusion: what does
$$\theta\begin{pmatrix}1 & 0& 0& \cdots & 0 \\ 0 & 1 & 0& \cdots & 0\end{pmatrix}(\Omega)$$ mean in this context? How are the matrix and $\Omega$ related to the coefficients of $a_0x^n+\cdots +a_n$?