Let \(f\) be entire and suppose the function \[ g(z)=\sqrt{f(z)} \] is also entire. Prove that \(f\) is constant.
An entire square root forces constancy — as extracted
P-WESCA13J-II3
- Area
- Complex Analysis
- Seen at
- WESLEYAN
- Years
- 2013
- Status
- draft
P-WESCA13J-II3
Let \(f\) be entire and suppose the function \[ g(z)=\sqrt{f(z)} \] is also entire. Prove that \(f\) is constant.