query: Existence of entire function s.t. for all $z\in\mathbb{C}$ with $|z|\geq 100:|f(z)|=|z|+1$
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: 35889
negative_passages.text: Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
negative_passages.docid: 51934
negative_passages.text: Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
negative_passages.docid: 10253
negative_passages.text: Proving that all entire & injective functions take the form $f = ax + b$?
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: 84313
negative_passages.text: $|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
negative_passages.docid: 123249
negative_passages.text: An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 82229
negative_passages.text: Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
negative_passages.docid: 145956
negative_passages.text: $f$ is entire without any zeros then there is an entire function $g$ such that $f=e^g$
negative_passages.docid: 13927
negative_passages.text: Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
negative_passages.docid: 131754
negative_passages.text: Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
negative_passages.docid: 128477
negative_passages.text: Entire function constant, where $f(z)=f(z+1)$ and $|f(z)|< e^{|z|}$.
negative_passages.docid: 50427
negative_passages.text: Is function $f:\mathbb C-\{0\}\rightarrow\mathbb C$ prescribed by $z\rightarrow \large \frac{1}{z}$ by definition discontinuous at $0$?
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 7755
negative_passages.text: Question on entire function
negative_passages.docid: 23585
negative_passages.text: Show that a holomorphic function satisfying $|f(z)|\leq c|z|^n$ must be $f(z)=a\cdot z^n$ for some a.