query: Is there an entire function satisfying $|f(z)|=|z|+1$ for every $|z|\geq2017$?
positive_passages.docid: 28011
positive_passages.text: Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
negative_passages.docid: 55138
negative_passages.text: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
negative_passages.docid: 84206
negative_passages.text: How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
negative_passages.docid: 2527
negative_passages.text: Entire function bounded by a polynomial is a polynomial
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$
negative_passages.docid: 17119
negative_passages.text: Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$
negative_passages.docid: 81758
negative_passages.text: Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero.
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 86473
negative_passages.text: Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
negative_passages.docid: 74245
negative_passages.text: Characterizing non-constant entire functions with modulus $1$ on the unit circle
negative_passages.docid: 74051
negative_passages.text: No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
negative_passages.docid: 94597
negative_passages.text: $f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
negative_passages.docid: 20955
negative_passages.text: 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 $z\in\mathbb{D}$,
negative_passages.docid: 99827
negative_passages.text: For what values will f(x) be necessarily one-one?
negative_passages.docid: 139614
negative_passages.text: Polynomial bounded real part of an entire function
negative_passages.docid: 98399
negative_passages.text: Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
negative_passages.docid: 65054
negative_passages.text: How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$