OPEN
Let $f(z)=\sum_{k\geq 1}a_k z^{n_k}$ be an entire function of finite order such that $\lim n_k/k=\infty$. Let $M(r)=\max_{\lvert z\rvert=r}\lvert f(z)\rvert$ and $m(r)=\max_n \lvert a_nr^n\rvert$. Is it true that
\[\limsup\frac{\log m(r)}{\log M(r)}=1?\]
A problem of Pólya. Results of Wiman
[Wi14] imply that if $(n_{k+1}-n_k)^2>n_k$ then $\limsup \frac{m(r)}{M(r)}=1$. Erdős and Macintyre
[ErMa54] proved this under the assumption that
\[\sum_{k\geq 2}\frac{1}{n_{k+1}-n_k}<\infty.\]