My friend recently gave me this system of functional equations, asking me if I could find holomorphic $f,g: \mathbb{C} \to \mathbb{C}$ satisfying:
- $g(g(f(z))) = z$
- $\displaystyle\prod_{f(x)=0}^{} g(x)=1$
To which I promptly said, “no.” Thoughts? Hints?
from Hot Weekly Questions - Mathematics Stack Exchange
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