Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Summer 2021 • Question 5

Question

Math 6220 • Complex Analysis Summer 2021 • Question 5

Suppose that \(f\) is entire and \(f(\mathbb {C})\subset \mathbb {C}\setminus [0,\infty )\), show that \(f\) is constant. Do not use either Picard Theorem (at least not without proof).

Raw LaTeX

Suppose that \(f\) is entire and \(f(\mathbb{C})\subset\mathbb{C}\setminus[0,\infty)\), show that \(f\) is constant.
Do not use either Picard Theorem (at least not without proof).

Topic Tags

Entire Functions and Liouville-Type Theorems Picard-Type Theorems and Casorati-Weierstrass