Characterize all entire functions $f$ such that $|f(z)|=1$, whenever $|z|=1$
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
33099
If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
63255
Proving an entire, complex function with below bounded modulus is constant.
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
99827
For what values will f(x) be necessarily one-one?
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
76971
Entire functions bounded along $\vert z\vert = R$
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
26353
Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
17310
Can $f(x)=|x|^3$ be differentiated
63701
An example of a regular function over an open set
65054
How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
36379
Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial.