An Introduction to the Theory of Automorphic Functions by Lester Ford
An Introduction to the Theory of Automorphic Functions - Table of Contents
1. Linear Transformations
2. Groups of Linear Transformations
3. Automorphic Functions
4. The Riemann–Schwarz Triangle Functions
5. Non-Euclidean Geometry
6. Uniformization
What You Will Learn in An Introduction to the Theory of Automorphic Functions
"An Introduction to the Theory of Automorphic Functions" by "Lester R. Ford" is a classical text that systematically introduces the study of "automorphic functions", complex functions invariant under groups of transformations. The book begins with the basics of linear fractional transformations, "Fuchsian groups", and their action on the complex plane. Ford carefully explains fundamental domains, providing the geometric foundation needed to understand how these transformations structure the behavior of complex functions.
Building on this foundation, Ford explores the construction of automorphic functions through "series expansions" such as Poincaré and theta series. He demonstrates how these functions remain unchanged under group actions and discusses their connection to "conformal mappings". The text also examines how automorphic functions relate to differential equations with regular singularities, showing the deep interplay between algebraic, geometric, and analytic structures in complex analysis.
Ford’s approach makes a highly abstract area accessible to readers with a background in complex analysis, bridging classical and modern perspectives. The book has historical significance as one of the first systematic treatments in English, laying the groundwork for further developments in the theory of modular forms, Riemann surfaces, and automorphic representations. Its clarity and rigor make it a foundational resource for students and researchers exploring the geometry and analysis of complex functions.
Book Details & Specifications
Title:
An Introduction to the Theory of Automorphic Functions by Lester Ford
Publisher:
G. Bell & Sons
Year:
1915
Pages:
118
Type:
PDF
Language:
English
ISBN-10 #:
1330351169
ISBN-13 #:
978-1330351161
License:
Public Domain Work
Amazon:
Amazon
About the Author: Lester Randolph Ford
The author Lester Randolph Ford
(1886–1967) was a prominent American mathematician known for his work in "complex analysis", "automorphic functions", and "modular forms". Educated at the University of Michigan, he later taught at the University of Michigan and Washington University in St. Louis, gaining recognition for his clear, systematic approach to advanced mathematics. Ford’s textbook "An Introduction to the Theory of Automorphic Functions" became a foundational resource, explaining "Fuchsian groups" and "series expansions" with rigor and clarity. His work bridged geometric and analytic perspectives, influencing generations of mathematicians studying the deep connections between transformation groups and complex function theory.
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