Explorations in Complex Functions /

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...

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Bibliographic Details
Main Authors:	Beals, Richard (Author), Wong, Roderick S. C. (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
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. Functions of a Complex Variable. Special Functions. Number Theory. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of 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.