Is it possible to prove for which $p$ does the sum
$$\sum_{n=0}^{\infty} e^{-b n^p}$$
have a natural boundary on the imaginary b axis?
Is it possible to prove for which $p$ does the sum
$$\sum_{n=0}^{\infty} e^{-b n^p}$$
have a natural boundary on the imaginary b axis?
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