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   Author  Topic: entire function and polynoials  (Read 8225 times)
MonicaMath
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entire function and polynoials  
« on: Feb 26th, 2009, 11:56am »
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Hi everybody...
 
I have a BIG problem that needs to solve:
 
if f(z) is an entire function with |f(z)<=B|z|^S, for all z in C,  
(1) Should S be an integer and why,
(2) can we write f  as: f(z)=A z^j, for some A in C, with |A|<=B.
 
please can one help me in soving this problem.
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Eigenray
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Re: entire function and polynoials  
« Reply #1 on: Feb 26th, 2009, 7:56pm »
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The conclusion should be that f(z) is a polynomial of degree no more than S.
 
Are you familiar with Liouville's theorem?  Try to generalize the proof there to show that ak = 0 for k > S.
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