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Automorphic Functions
Lester R. Ford

AMS Chelsea Publishing
1951; 333 pp; hardcover
Volume: 85
ISBN-10: 0-8218-3741-9
ISBN-13: 978-0-8218-3741-2
List Price: US$41
Member Price: US$36.90
Order Code: CHEL/85.H
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Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (1929), it was welcomed for its elegant treatment of groups of linear transformations and for the remarkably clear and explicit exposition throughout the book. Ford's extraordinary talent for writing has been memorialized in the prestigious award that bears his name. The book, in the meantime, has become a recognized classic.

Ford's approach is primarily through analytic function theory. The first part of the book covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincaré theta series. The second part of the book covers conformal mappings, uniformization, and connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.


Graduate students and research mathematicians.


"This book is the first containing an extensive systematic treatment of the theory of automorphic functions in English. The author has succeeded in presenting this difficult subject in a manner which makes it accessible to those who are familiar with the fundamentals of the theory of functions of a complex variable. ... The first chapter, entitled 'Linear Transformations,' and the second, 'Groups of Linear Transformations,' give an especially clear treatment of topics which are of great importance in later work."

-- Fred W. Perkins, American Mathematical Monthly

"The exposition is remarkably clear and explicit ... a very simple and elegant treatment of groups of linear transformations, their fundamental regions and the functions invariant under the groups ... Professor Ford's work, in the first part of his book, is not mere exposition. The methods which he creates are original, and of permanent scientific value ... The second half of the book gives a detailed account of conformal mapping and uniformization, and considers some of the relations of automorphic functions to differential equations."

-- Bulletin of the AMS

Table of Contents

  • Linear transformations
  • Groups of linear transformations
  • Fuchsian groups
  • Automorphic functions
  • The Poincaré theta series
  • The elementary groups
  • The elliptic modular functions
  • Conformal mapping
  • Uniformization. Elementary and Fuchsian functions
  • Uniformization. Groups of Schottky type
  • Differential equations
  • A bibliography of automorphic functions
  • Author index
  • Subject index
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