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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods

Fall 2023 • Question 3

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods Fall 2023 • Question 3

Let \(f(z)\) be an entire function, and suppose there exists a non-negative constant \(C\) such that \(|f(z)|\le C|z|\) for every \(z\). Prove that \(f(z)=Az\), where \(A\) is a constant.

Raw LaTeX

Let \(f(z)\) be an entire function, and suppose there exists a non-negative constant \(C\) such
that \(|f(z)|\le C|z|\) for every \(z\). Prove that \(f(z)=Az\), where \(A\) is a constant.

Topic Tags

Entire Functions and Liouville's Theorem