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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2022 • Question 2

Question

Math 6220 • Complex Analysis Fall 2022 • Question 2

Show that if \(f\) is holomorphic on an open neighborhood of \(\overline {\mathbb {D}}\) and \(|f(z)|=1\) on \(|z|=1\) then \(f\) is a rational function.

Raw LaTeX

Show that if \(f\) is holomorphic on an open neighborhood of \(\overline{\mathbb{D}}\) and \(|f(z)|=1\)
on \(|z|=1\) then \(f\) is a rational function.

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Meromorphic Functions and Rational Functions Zeros of Holomorphic Functions and the Identity Theorem