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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2011 • Question 7

Question

Math 6210 • Real Analysis Spring 2011 • Question 7

Let \(f\) be a meromorphic function on \(\mathbb C\) such that there exist \(R,C>0\) and a positive integer \(k\) such that \(|f(z)|\le C|z|^k\) for all \(|z|\ge R\). Prove that \(f\) is a rational function.

Raw LaTeX

Let \(f\) be a meromorphic function on \(\mathbb C\) such that there
exist \(R,C>0\) and a positive integer \(k\) such that
\(|f(z)|\le C|z|^k\) for all \(|z|\ge R\). Prove that \(f\) is a rational function.

Topic Tags

Meromorphic Functions and Rational Functions