By William A. Veech
Author William A. Veech, the Edgar Odell Lovett Professor of arithmetic at Rice college, provides the Riemann mapping theorem as a unique case of an life theorem for common protecting surfaces. His specialise in the geometry of complicated mappings makes widespread use of Schwarz's lemma. He constructs the common protecting floor of an arbitrary planar area and employs the modular functionality to strengthen the theorems of Landau, Schottky, Montel, and Picard as results of the lifestyles of convinced coverings. Concluding chapters discover Hadamard product theorem and top quantity theorem.
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A Second Course in Complex Analysis (Dover Books on Mathematics) by William A. Veech