Complex Analysis with Applications to Number Theory

Introduction And Preliminaries.- Cauchy Theorems and Their Applications.-  Conformal Mappings and Riemann Mapping Theorem.- Picard's Theorems.- Factorisation of Analytic Functions in C and in a Region.- Gamma Function.- Riemann Zeta Function.- Dirichlet Series and Dirichlet Theorem.- Harmonic Functions.- Elliptic Functions and Modular Forms.

TARLOK NATH SHOREY is a distinguished professor at the National Institute of Advanced Studies (situated in the campus of the Indian Institute of Science), Bengaluru, India. Earlier, he taught at the Department of Mathematics, Indian Institute of Technology Bombay, India. He also had been associated with the Tata Institute of Fundamental Research (TIFR), Mumbai, India, for a period of 42 years. Professor Shorey has done numerous momentous works on transcendental number theory and Diophantine equation. In 1987, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology—the highest science award in India—in the Mathematical Sciences category. He has coauthored a book, Exponential Diophantine Equations, and has more than 142 research publications to his credit. He is fellow of the Indian National Science Academy (INSA), Indian Academy of Sciences (IASc) and The National Academy of Sciences (NASI).