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Uniformization of simply connected finite type log-Riemann surfaces

Complex Variables 2010-11-04 v1

Abstract

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.

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Cite

@article{arxiv.1011.0812,
  title  = {Uniformization of simply connected finite type log-Riemann surfaces},
  author = {Kingshook Biswas and Ricardo Perez-Marco},
  journal= {arXiv preprint arXiv:1011.0812},
  year   = {2010}
}

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13 pages