ADVANCED COMPLEX ANALYSIS (Optional paper)

Schwarz’s Lemma and its consequences, Doubly periodic entire functions, Fundamental theorem of Algebra, Zeros of certain polynomials.                                                     

Meromorphic functions, Essential Singularities and Picard’s Theorem, Analytic Continuation, Monodrmy theorem, Poisson integral formula, Analytic continuation via reflexion.

Infinite sums and infinite product of complex numbers, Infinite product of analytic functions, Factorization of entire functions.                                                                                         

The Gamma functions, The Zeta functions, Jensen Formula, The order and the Genus of entire functions. Open mapping theorem and Hurwitz’ theorem, Basic results on univalent functions. 

 Normal families, The Riemann mapping theorem, Biberbach Conjecture, The Bloch-Landau Theorem, Picard’s Theorem Open mapping theorem and Hurwitz’ theorem, Basic results on univalent functions.