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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2018 • Question 7

Question

Math 6210 • Real Analysis Fall 2018 • Question 7

Either prove that there is no entire function \(f\) so that \(f(n)=0\) for all \(n\in \mathbb N\) and \(f(z)\ne 0\) for all \(z\in \mathbb C\setminus \mathbb N\), or give an example of such a function with justification.

Raw LaTeX

Either prove that there is no entire function \(f\) so that
\(f(n)=0\) for all \(n\in\mathbb N\) and \(f(z)\ne0\) for all
\(z\in\mathbb C\setminus\mathbb N\), or give an example of such a function
with justification.

Topic Tags

Entire Functions and Liouville-Type Theorems