Erdős Problems 514

### What is the conjecture

https://www.erdosproblems.com/514

Let $f(z)$ be an entire transcendental function. Does there exist a path $L$ so that, for every $n$,
$$\lvert f(z)/z^n\rvert \to \infty$$
as $z\to \infty$ along $L$?

Can the length of this path be estimated in terms of $M(r)=\max_{\lvert z\rvert=r}\lvert f(z)\rvert$? Does there exist a path along which $\lvert f(z)\rvert$ tends to $\infty$ faster than a fixed function of $M(r)$ (such that $M(r)^\epsilon$)?

Status: open

### 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