query: Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
positive_passages.docid: 74245
positive_passages.text: Characterizing non-constant entire functions with modulus $1$ on the unit circle
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: 110704
negative_passages.text: Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
negative_passages.docid: 62966
negative_passages.text: Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
negative_passages.docid: 15001
negative_passages.text: Multiple choice question: Let $f$ be an entire function such that $\lim_{|z|\rightarrow\infty}|f(z)|$ = $\infty$.
negative_passages.docid: 26353
negative_passages.text: Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
negative_passages.docid: 44670
negative_passages.text: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
negative_passages.docid: 55138
negative_passages.text: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
negative_passages.docid: 76971
negative_passages.text: Entire functions bounded along $\vert z\vert = R$
negative_passages.docid: 76285
negative_passages.text: Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
negative_passages.docid: 86128
negative_passages.text: Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
negative_passages.docid: 73519
negative_passages.text: Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
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: 124971
negative_passages.text: Find all holomorphic functions with $\Re(f(x+iy))=2xy$
negative_passages.docid: 52858
negative_passages.text: Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
negative_passages.docid: 107518
negative_passages.text: Entire function $f$ such that $|f(z)| ≤ K |z|^3$ for $|z|\ge1$ and $f(z) = f(iz)$ for every $z∈C$