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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Summer 2022 • Question 7

Question

Math 6220 • Complex Analysis Summer 2022 • Question 7

Prove or disprove: There is no nonconstant entire function satisfying

\[ \operatorname {Re}(f(z))<\operatorname {Im}(f(z)) \]

for all \(z\). In your solution don’t quote either Picard theorem.

Raw LaTeX

Prove or disprove: There is no nonconstant entire function satisfying

\[
\operatorname{Re}(f(z))<\operatorname{Im}(f(z))
\]

for all \(z\). In your solution don't quote either Picard theorem.

Topic Tags

Entire Functions and Liouville-Type Theorems Maximum Modulus Principle Picard-Type Theorems and Casorati-Weierstrass