Short Course in Automorphic Functions (Athena S.) - Hardcover
This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. The text begins with the basics of Fuchsian groups, advancing to the development of Poincaré series and automorphic forms and concluding with the connection between the theory of Riemann surfaces with theories of automorphic forms and discontinuous groups.
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About the Author:
This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincare, employing the model of the hyperbolic plane. The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincare series. Formulas for divisors of a function and form are proved and their consequences analyzed. The final chapter is devoted to the connection between automorphic function theory and Riemann surface theory, concluding with some applications of Riemann-Roch theorem.
The book presupposes only the usual first courses in complex analysis, topology, and algebra. Exercises range from routine verifications to significant theorems. Notes at the end of each chapter describe further results and extensions, and a glossary offers definitions of terms.
Dover (2014) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1966.
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Joseph Lehner taught at Michigan State University, the University of Maryland at College Park, and the University of Pittsburgh.
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- PublisherHolt,Rinehart & Winston of Canada Ltd
- Publication date1966
- ISBN 10 0030524709
- ISBN 13 9780030524707
- BindingHardcover
- Number of pages144
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