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Let $f(z)=\sum_{k=1}^\infty a_kz^{n_k}$ be an entire function. Is it true that if $n_k/k\to \infty$ then $f(z)$ assumes every value infinitely often?
#517
:
[Er61,p.250]
analysis
A conjecture of Fejér and Pólya. Fejér
[Fe08]
proved that if $\sum\frac{1}{n_k}<\infty$ then $f(z)$ assumes every value at least once, and Biernacki
[Bi28]
showed that this holds under the assumption that $n_k/k\to \infty$.
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