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Let $f(z)$ be an entire function, not a polynomial. Does there exist a path $C$ such that, for every $\lambda>0$, the integral \[\int_C \lvert f(z)\rvert^{-\lambda} \mathrm{d}z\] is finite?
Huber [Hu57] proved that for every $\lambda>0$ there is a path $C_\lambda$ such that this integral is finite.