Abstract:
In the work for the theta function
$$
\theta(z)=\theta(z;q)=\sum\limits_{n=-\infty}^{\infty}e^{2izn}q^{n^2}
$$
identity
\begin{gather*}
\theta(z_1+w)\dots\theta(z_{k-1}+w)\theta(z_1+\dots+z_{k-1}-w)=\sum\limits_{i=1}^{s}\varphi_i(z_1,\dots,z_{k-1})\psi_i(w) \\
(\forall z_1,\dots, z_{k-1}, w \in \mathbb{C})
\end{gather*}
with some clearly indicates theta functions $\psi_i$ of one variable and functions $\varphi_i$ of $k-1$ variables is proved.
Fulltext:
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