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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2008 • Question 9

Question

Math 6210 • Real Analysis Spring 2008 • Question 9

Let \(f\) be a non-constant meromorphic function on \(\mathbb C\). Show that either there exists a sequence \(z_n\to \infty \) with \(f(z_n)\to 0\) as \(n\to \infty \) or there is a \(z\in \mathbb C\) such \(f(z)=0\).

Raw LaTeX

Let \(f\) be a non-constant meromorphic function on \(\mathbb C\).
Show that either there exists a sequence \(z_n\to\infty\) with
\(f(z_n)\to0\) as \(n\to\infty\) or there is a \(z\in\mathbb C\) such \(f(z)=0\).

Topic Tags

Lp Spaces and Sequence Spaces Meromorphic Functions and Rational Functions