Entire function with positive real part is constant (no Picard)
17408
An entire function whose real part is bounded must be constant.
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
96539
is $f$ constant or dilation
97579
showing a function defined from an integral is entire
113343
$f$ is constant if derivative equals zero
3818
Proving two entire functions are constant.
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
120676
A certain element which makes functionals positive
76971
Entire functions bounded along $\vert z\vert = R$
34719
Show this holomorphic function is constant
727
Prove that any continuous integer-valued function of a real variable is constant.
5416
How does one prove if a multivariate function is constant?
82745
Showing Entire Function is Bounded
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
141863
If the imaginary part of an entire function is never zero, the function is constant
153855
Complex analysis, showing a function is constant
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