Advanced Complex Analysis

Series and product developments: Power series expansions, Partial fractions and factorizations; Entire functions: The Hadamard’s theorem, Jensen’s formula, The Riemann zeta function; Normal families: Equicontinuity, Normality and compactness, Arzela’s theore; Analytic continuation and Riemann surfaces: Germs and sheaves, Analytic continuations along arcs, Homotopic curves, The monodromy theorem, Branch points, Algebraic functions; Picard’s theorem: Lacunary values; The Reimann mapping theorem;The Dirichlet problem; Canonical mappings of multiply connected regions; Elliptic functions and Weierstrass Theory; Basic results on univalent functions; The range of analytic functions: Bloch’s theorem, Schottky’s theorem;