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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2014 • Question 6

Question

Math 6210 • Real Analysis Fall 2014 • Question 6

Let \(f\) be a nonzero entire function. Assume that the set \(Z(f)=\{z\in \mathbb C:\ f(z)=0\}\) is unbounded. Show that \(f\) had an essential singularity at \(\infty \).

Raw LaTeX

Let \(f\) be a nonzero entire function. Assume that the set
\(Z(f)=\{z\in\mathbb C:\ f(z)=0\}\) is unbounded. Show that \(f\) had an essential
singularity at \(\infty\).

Topic Tags

Entire Functions and Liouville-Type Theorems Isolated Singularities and Residues Zeros of Holomorphic Functions and the Identity Theorem