Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2019 • Question 8

Question

Math 6210 • Real Analysis Fall 2019 • Question 8

Prove that if an entire function is not a polynomial then there is a number \(z\) so that the cardinality of \(f^{-1}(z)\) is infinite.

Do not use Picard’s theorems.

Raw LaTeX

Prove that if an entire function is not a polynomial then there
is a number \(z\) so that the cardinality of \(f^{-1}(z)\) is infinite.

\textbf{Do not use Picard's theorems.}

Topic Tags

Entire Functions and Liouville-Type Theorems Picard-Type Theorems and Casorati-Weierstrass