Explorations in Complex Functions [electronic resource] by Richard Beals, Roderick S. C. Wong.

This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysi...

Full description

Bibliographic Details
Uniform Title:Graduate Texts in Mathematics, 2197-5612 ; 287
Main Authors: Beals, Richard (Author)
Wong, Roderick S. C. (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2020.
Edition:1st ed. 2020.
Series:Graduate Texts in Mathematics, 287
Subjects:
Functions of complex variables.
Special functions.
Number theory.
Online Access:
Springer Mathematics and Statistics eBooks 2020 English/International: 2020 (Springer Link)
Format: Electronic eBook
Contents:
  • 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 Phragmén–Lindelöf and Paley–Wiener
  • Theorems of Wiener and Lévy; the Wiener–Hopf method
  • Tauberian theorems
  • Asymptotics and the method of steepest descent
  • Complex interpolation and the Riesz–Thorin theorem.