Show an entire function with $f(z) = f(z+1), f(z) = f(z+i), $for all $z \in \mathbb{C}$ is constant
7878
Proving that a doubly-periodic entire function $f$ is constant.
35787
An entire function with a bound on its integral is constant
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
135772
how to show image of a non constant entire function is dense in $\mathbb{C}$?
122356
Complex Analysis, Entire functions
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
103340
Show that this entire function is polynomial.
27251
Holomorphic function with $f\circ f=f$
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
158561
Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
99894
Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
10727
Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.
75638
Let $u:\mathbb{C}\rightarrow\mathbb{R}$ be a harmonic function such that $0\leq f(z)$ for all $ z \in \mathbb{C}$. Prove that $u$ is constant.
65054
How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
27772
Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.