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The problem is as follows:

Suppose $f$ entire satisfying $$ |f(z)| \leq A + B |z|^{3/2} $$ for some fixed $A,B > 0$. Prove that $f$ is a linear polynomial.

I know I want to reduce it to a function where I can use a Cauchy bound, but I'm not sure how.

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    I think the description "polynomial of degree $3/2$" for this bound is rather unusual.2012-11-02
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    Let $f(z) = a_0 + a_1z + a_2z^2 + \cdots$ be the Taylor expansion of $f$ around the origin. To show $f$ is a linear polynomial, you must show $a_2 = 0$, $a_3 = 0$, etc. What do the Cauchy estimates say about the size of these coefficients?2012-11-02
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    possible duplicate of [if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?](http://math.stackexchange.com/questions/151700/if-f-is-entire-and-fz-leq-1z1-2-why-must-f-be-constant)2012-11-02

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