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regularity of root spacing of $G(z)=\sum\limits_{n=1}^{\infty} \frac{e^{-n^{2}}}{n^{z}}$
Define, on $\mathbb{C}$:
$$G(z)=\sum_{n=1}^{\infty} \frac{e^{-n^{2}}}{n^{z}}$$
A domain colored portrait of $G(z)$ (boxes are supposed to be negative signs):
suggests that the roots of $G(z)$ are ...
