Determine all entire functions $f$ with the property that if $|z|=1$, then $|f(z)|=1$.
117848
Find all entire functions
38568
Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
20047
At $z=0$ the function $f(z)=\exp({z\over 1-\cos z})$ has
10253
Proving that all entire & injective functions take the form $f = ax + b$?
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
67848
Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties.
152347
Proof that a certain entire function is a polynomial
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
99894
Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number
15001
Multiple choice question: Let $f$ be an entire function such that $\lim_{|z|\rightarrow\infty}|f(z)|$ = $\infty$.
94597
$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$