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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods

Summer 2024 • Question 3

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods Summer 2024 • Question 3

Let \(f\) be an entire function, with \(|f(z)|\le C|z|^2\) for all \(z\), where \(C\) is a constant. Show that \(f(z)=az^2+bz\) for some constants \(a,b\).

Raw LaTeX

Let \(f\) be an entire function, with \(|f(z)|\le C|z|^2\) for all \(z\), where \(C\) is a constant. Show
that \(f(z)=az^2+bz\) for some constants \(a,b\).

Topic Tags

Entire Functions and Liouville's Theorem