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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2014 • Question 8

Question

Math 6210 • Real Analysis Fall 2014 • Question 8

Let \(f\) be an entire function and \(n\) a positive integer. Show that there exists an entire function \(g\) such that \(f=g^n\) if and only if the order of each zero of \(f\) is divisible by \(n\).

Raw LaTeX

Let \(f\) be an entire function and \(n\) a positive integer. Show
that there exists an entire function \(g\) such that \(f=g^n\) if and only if the
order of each zero of \(f\) is divisible by \(n\).

Topic Tags

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