Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Summer 2021 • Question 1

Question

Math 6220 • Complex Analysis Summer 2021 • Question 1

Show that any function which is meromorphic on the Riemann sphere, \(\widehat {\mathbb {C}}=\mathbb {C}\cup \{\infty \}\), is either constant or can be written as the sum of the singular parts of its Laurent series at its poles, in particular conclude that the function is rational.

Raw LaTeX

Show that any function which is meromorphic on the Riemann sphere,
\(\widehat{\mathbb{C}}=\mathbb{C}\cup\{\infty\}\), is either constant or can be written as the sum of the
singular parts of its Laurent series at its poles, in particular conclude that
the function is rational.

Topic Tags

Isolated Singularities and Residues Laurent Series and Annuli Meromorphic Functions and Rational Functions