### MA6120 ADVANCED COMPLEX ANALYSIS

#### Course Details

Analytic Continuation: Direct Analytic Continuation, Monodromy Theorem, Poisson Integral Formula, Analytic Continuation via Reflection,

Representations for Meromorphic and Entire Functions: Infinite Sums and Meromorphic functions, Infinite Product of Complex Numbers, Infinite Products of Analytic Functions, Factorization of Entire Functions,The Gamma Function, The Zeta Function Jensen's Formula, The Order and the Genus of Entire Functions.

Mapping Theorems: Open Mapping Theorem and Hurwitz' Theorem, Basic Results on Univalent Functions, Normal Families, The Riemann Mapping Theorem, Bieberbach Conjecture, The Bloch-Landau Theorems Picard's Theorem.

#### Course References:

Books:

1. L. Ahlfors: Complex Analysis, 2nd ed., McGraw-Hill,New York, 1966.

2. T.W. Gamelin: Complex Analysis, Springer-Verlag, 2001.

3. S. Ponnusamy, S.: Foundations of Complex Analysis, 2nd ed., Narosa Publishing House, 508 pp., India (2005)

4. S. Ponnusamy and H. Silverman, Complex Variables with Applications, 2006, 524 pp, Birkhaeuser, Boston.