Find all holomorphic functions $f: \mathbb{C} \rightarrow \mathbb{C}$ such that, for all $x,y\ \epsilon \ \mathbb{R} $ , $Re(f(x+iy)) := 2xy$
124971
Find all holomorphic functions with $\Re(f(x+iy))=2xy$
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
86473
Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
63446
The existence of analytical branch of the logarithm of a holomorphic function
83014
Holomorphic function interpolating $e^{-n}$
59745
Behavior of holomorphic functions on the boundary of the unit disk
4698
Gamma Function Holomorphic
82229
Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
50115
Show that the holomorphic function $u + iv$ must be constant if $u = h \circ v$. Problem from Remmert.
13728
can $f$ be holomorphic?
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
12239
Holomorphic function with a fixed point
40336
Existence of Holomorphic function (Application of Schwarz-Lemma)
74891
sum of holomorphic functions
155244
Holomorphic self map on the open unit disc
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
106175
A function is analytic if and only if it is holomorphic