entire function with constant modulus on circle -Schwarz reflection principle
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
108846
Estimate of analytic function in a unit disk
105172
Prove that the entire function is constant over certain conditions.
115863
Every harmonic function is the real part of a holomorphic function
4084
Does there exist a holomorphic function with the following property?
9748
Maximum modulus principle for an unbounded function in the half right plane
7878
Proving that a doubly-periodic entire function $f$ is constant.
5440
Maximum of sum of finite modulus of analytic function.
141863
If the imaginary part of an entire function is never zero, the function is constant
153855
Complex analysis, showing a function is constant
14117
Holomorphic function has at most countably zeros
93400
Prove that an analytic function with a constant imaginary part is constant itself
74527
Expressing the area of the image of a holomorphic function by the coefficients of its expansion
139614
Polynomial bounded real part of an entire function
31736
Removable singularities and an entire function
138809
Consequences of a fixed point of a bounded, complex analytic function
17408
An entire function whose real part is bounded must be constant.