Generalized Bieberbach conjectures ? tommy1729 Ultimate Fellow Posts: 1,742 Threads: 382 Joined: Feb 2009 08/12/2013, 08:11 PM I wanted to say that I believe tetration is related to generalizations of the Bieberbach conjecture/de Branges theorem , Koebe quarter theorem and related. For instance Let U be the unit circle , let V be a smaller circle that touches the unit circle from the inside. The "moonshaped " area ( this has a name right ? ) Is called A. Let the open set A be mapped injectively to the complex plane by the function f(z). Then D^n f(z) dz satisfies .... Now by riemann mappings and inversing functions we end up with a branch for a superfunction. And the conjectured properties must be carried along in a transformed way. This "moonshaped conjecture " might already have a name , but if not I call it tommy's moonshine conjecture for now , although I havent figured out the details of even the precise statement. This is something I have not seen adressed on the forum yet so I found it necc to mention it. regards tommy1729 « Next Oldest | Next Newest »

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