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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2023 • Question 5

Question

Math 6220 • Complex Analysis Fall 2023 • Question 5

Let \(f\) be an entire function and suppose that for every positive integer \(n>1\) and every \(z\in \mathbb {C}\) with \(|z|<n\) we have

\[ |f'(z)|<n^2\log n \]

Does this imply that \(f\) is a polynomial?

Raw LaTeX

Let \(f\) be an entire function and suppose that for every positive integer
\(n>1\) and every \(z\in\mathbb{C}\) with \(|z|<n\) we have

\[
|f'(z)|<n^2\log n
\]


Does this imply that \(f\) is a polynomial?

Topic Tags

Entire Functions and Liouville-Type Theorems