Henri Poincaré proved that the map f is essentially unique: if z0 is an element of U and φ is an arbitrary angle, then there exists precisely one f as above such that f(z0) = 0 and that the argument of the derivative of f at the point z0 is equal to φ.
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Reinhold Remmert (1998) Classical topics in complex function theory, Springer-Verlag, ISBN 0-387-98221-3
Bernhard Riemann | Liouville's theorem | Riemann zeta function | Riemann surface | Riemann hypothesis | Chinese remainder theorem | Shannon–Hartley theorem | Riemann sphere | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Texture mapping | Szemerédi's theorem | Semantic mapping | Schottky's theorem | Riemann solver | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Hugo Riemann | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions |