Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2006 • Question 7

Question

Math 6210 • Real Analysis 2006 • Question 7

Prove that if an entire function \(f\) satisfies an inequality of the form \[ |f(z)|\le A+B\log |f(z)| \] for some positive constants \(A\) and \(B\) and for all \(z\in \mathbb C\), then \(f\) is a constant.

Raw LaTeX

Prove that if an entire function \(f\) satisfies an inequality of the
form
\[
|f(z)|\le A+B\log |f(z)|
\]
for some positive constants \(A\) and \(B\) and for all \(z\in\mathbb C\), then \(f\) is
a constant.

Topic Tags

Entire Functions and Liouville-Type Theorems