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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2018 • Question 7

Question

Math 6210 • Real Analysis Spring 2018 • Question 7

Let \(f\) be a nonconstant entire function. Assume that the set \[ \{z\in \mathbb C:|f(z)|<1\} \] is unbounded. Show that \(f\) has an essential singularity at \(\infty \).

Raw LaTeX

Let \(f\) be a nonconstant entire function. Assume that the set
\[
\{z\in\mathbb C:|f(z)|<1\}
\]
is unbounded. Show that \(f\) has an essential singularity at \(\infty\).

Topic Tags

Entire Functions and Liouville-Type Theorems Isolated Singularities and Residues