Advanced complex analysis
著者
書誌事項
Advanced complex analysis
（A comprehensive course in analysis, pt. 2B）
American Mathematical Society, c2015
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 2B provides a comprehensive look at a number of subjects of complex analysis not included in Part 2A. Presented in this volume are the theory of conformal metrics (including the Poincare metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painleve smoothness theorem), topics in analytic number theory (including Jacobi's two- and four-square theorems, the Dirichlet prime progression theorem, the prime number theorem, and the Hardy-Littlewood asymptotics for the number of partitions), the theory of Fuschian differential equations, asymptotic methods (including Euler's method, stationary phase, the saddle-point method, and the WKB method), univalent functions (including an introduction to SLE), and Nevanlinna theory. The chapters on Fuschian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.
目次
Riemannian metrics and complex analysis
Some topics in analytic number theory
Ordinary differential equations in the complex domain
Asymptotic methods
Univalent functions and Loewner evolution
Nevanlinna theory
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
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