Mathematics – Complex Variables
Scientific paper
2010-11-03
Mathematics
Complex Variables
13 pages
Scientific paper
We consider simply connected log-Riemann surfaces with a finite number of ramification points. We prove that these surfaces are biholomorphic to C with uniformizations given by entire functions of the form F (z) = \int Q(z) e^{P(z)} dz where P, Q are polynomials of degrees equal to the number of infinite and finite order ramification points respectively. Conversely any such entire function defines a simply connected log-Riemann surface with finitely many ramification points.
Biswas Kingshook
Pérez-Marco Ricardo
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