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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2021 • Question 7

Question

Math 6220 • Complex Analysis Fall 2021 • Question 7

Show that if \(f,g:B(0,1)\setminus \{0\}\to \mathbb {C}\) are holomorphic, \(f\) has an essential singularity at 0 and \(g\) has a pole at 0 then \(\frac {g}{f}\) has an essential singularity at 0.

Raw LaTeX

Show that if \(f,g:B(0,1)\setminus\{0\}\to\mathbb{C}\) are holomorphic, \(f\) has an essential
singularity at 0 and \(g\) has a pole at 0 then \(\frac{g}{f}\) has an essential singularity at 0.

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Isolated Singularities and Residues Zeros of Holomorphic Functions and the Identity Theorem