Explorations in Complex Functions (Paperback)

Basics.- Linear Fractional Transformations.- Hyperbolic geometry.- Harmonic Functions.- Conformal maps and the Riemann mapping theorem.- The Schwarzian derivative.- Riemann surfaces and algebraic curves.- Entire functions.- Value distribution theory.- The gamma and beta functions.- The Riemann zeta function.- L-functions and primes.- The Riemann hypothesis.- Elliptic functions and theta functions.- Jacobi elliptic functions.- Weierstrass elliptic functions.- Automorphic functions and Picard's theorem.- Integral transforms.- Theorems of Phragmen?Lindelof and Paley?Wiener.- Theorems of Wiener and Levy; the Wiener?Hopf method.- Tauberian theorems.- Asymptotics and the method of steepest descent.- Complex interpolation and the Riesz?Thorin theorem.