If $f:\mathbb{C}\to\mathbb{C}$ is Entire and $\vert f \vert\le A+B\vert z \vert^{3/2}$, then $f$ is Linear
1954
Entire function bounded by polynomial of degree 3/2 must be linear.
3818
Proving two entire functions are constant.
127198
What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
122356
Complex Analysis, Entire functions
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
126808
Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
46514
Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
149849
Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
53528
If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
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.
94190
Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”
146506
If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
68071
If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.