Erdős Problem 515

### What is the conjecture

https://www.erdosproblems.com/515

Let $f(z)$ be an entire function, not a polynomial. Does there exist a locally rectifiable path $C$ tending to infinity such that, for every $\lambda>0$, the integral
$$\int_C \lvert f(z)\rvert^{-\lambda} \mathrm{d}z$$
is finite?

Status: solved

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else