ComplexAnalysis2010aug

# ComplexAnalysis2010aug - n 1. 3. Are there any entire...

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Qualifying Exam, Complex Analysis, August 2010 1. Let n > 0 be an integer. How many solutions does the equation 3 z n = e z have in the open unit disk? Justify your answer in full detail. 2. Let f ( z ) = n 0 a n z n be holomorphic in the unit disk U such that | f 0 ( z ) | ≤ 1 1 - | z | , z U. Prove that | a n | ≤ e for all
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Unformatted text preview: n 1. 3. Are there any entire functions f which satisfy | f ( z ) | p | z | for all z C ? Justify your answer in full detail. 4. Show that the function I ( z ) = Z + - e-( t-z ) 2 dt , z C , is constant. 1...
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## This note was uploaded on 06/19/2011 for the course MATH 680 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.

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