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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 8

Question

Math 6210 • Real Analysis 2005 • Question 8

Fix positive integers \(k\) and \(l\). Describe the space of meromorphic functions on the Riemann sphere that have a have a pole of order at most \(k\) at \(\infty \) and a zero of order at least \(l\) at the origin.

Raw LaTeX

Fix positive integers \(k\) and \(l\). Describe the space of
meromorphic functions on the Riemann sphere that have a have a pole of order at
most \(k\) at \(\infty\) and a zero of order at least \(l\) at the origin.

Topic Tags

Isolated Singularities and Residues Meromorphic Functions and Rational Functions Zeros of Holomorphic Functions and the Identity Theorem