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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2013 • Question 6

Question

Math 6210 • Real Analysis Fall 2013 • Question 6

Let \(f\) and \(g\) be analytic functions defined on an open set \(U\subset \mathbb C\). Assume that \(g\) is not identically equal to zero. Prove that \(F=f/g\) does not have essential singularities in \(U\).

Raw LaTeX

Let \(f\) and \(g\) be analytic functions defined on an open set
\(U\subset\mathbb C\). Assume that \(g\) is not identically equal to zero. Prove
that \(F=f/g\) does not have essential singularities in \(U\).

Topic Tags

Analytic Continuation and Monodromy Holomorphic Functions and Cauchy-Riemann Equations Isolated Singularities and Residues Zeros of Holomorphic Functions and the Identity Theorem