# theta in zeta

Let $\phi=(1+\sqrt{5})/2$, then consider
$V(z)=\sum_{n=1}^{\infty} \frac{\theta_{1}(z, e^{-\pi\phi n})}{n^{z}}$

Remarks on $V(z)$:
It is reminiscent of a Clausen function, but I have, a la “The Jacobi theta functions are the elliptic analogs of the exponential function”, replaced the trigonmetric function with a Jacobi theta function. I see that there are some references to “q-Clausen functions”, but I can’t get at them. So have some domain colored pictures, which may or may not be accurate: