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Let $f$ an entire function whose only zeros are all the negative integers. Is possible that $f$ satisfies $|f(z)|\leq C_1 e^{C_2 |z|^p},$ for some real constants $C_1, C_2,$ and $p<1$?

Any help?

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1 Answer 1

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Hint: Multiply the given function with the Gamma Function, and then study the growth rate.

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  • $\begingroup$ Thanks for the hint, but I don't see why it helps. Would be happy for further explanation. $\endgroup$
    – user95747
    Commented Jul 16, 2016 at 20:23

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