Buch, Englisch
Reihe: AMS Chelsea Publishing
Buch, Englisch
Reihe: AMS Chelsea Publishing
ISBN: 978-0-8218-3741-2
Verlag: American Mathematical Society
When published in 1929, Ford's book was the first treatise in English on automorphic functions. By this time the field was already fifty years old, as marked from the time of Poincare's early Acta papers that essentially created the subject. The work of Koebe and Poincare on uniformization appeared in 1907. In the seventy years since its first publication, Ford's Automorphic Functions has become a classic. His approach to automorphic functions is primarily through the theory of analytic functions. He begins with a review of the theory of groups of linear transformations, especially Fuchsian groups. He covers the classical elliptic modular functions, as examples of non-elementary automorphic functions and Poincare theta series. Ford includes an extended discussion of conformal mappings from the point of view of functions, which prepares the way for his treatment of uniformization. The final chapter illustrates the connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.
Contents
- Linear transformations
- Groups of linear transformations
- Fuchsian groups
- Automorphic functions
- The Poincare 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
- Linear transformations
- Groups of linear transformations
- Fuchsian groups
- Automorphic functions
- The Poincare 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
Zielgruppe
Graduate students and research mathematicians.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
