I was reading Ahlfors' and came across the "genus of the canonical product." I'm curious if there's any relationship between this genus and the genus of a torus(if so, my best guess is that these form a level set on a torus of the same genus). Or, is this just a case of, "we needed a name, and everything's been taken?"
Just to be clear, what I'm referencing is pg 196:
"The preceding proof has shown that the product
$$ (22) \hspace{0.5cm}\prod_{1}^{\infty}\left(1-\frac{z}{a_{n}}\right) e^{\frac{z}{a_{n}}+\frac{1}{2}\left(\frac{z}{a_{n}}\right)^{2}+\cdots+\frac{1}{h}\left(\frac{z}{a_{n}}\right)^{h}} $$ converges and represents an entire function provided that the series $\sum_{n=1}^{\infty}\left(R /\left|a_{n}\right|\right)^{h+1} /(h+1)$ converges for all $R,$ that is to say provided that $\Sigma 1 /\left|a_{n}\right|^{h+1}<\infty .$ Assume that $h$ is the smallest integer for which this series converges; the expression (22) is then called the canonical product associated with the sequence $\left\{a_{n}\right\},$ and $h$ is the genus of the canonical product."