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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online