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A Short Course in Automorphic Functions (Dover Books on Mathematics) - Softcover

 
9780486789743: A Short Course in Automorphic Functions (Dover Books on Mathematics)
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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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From the Back Cover:

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 Poincaré, 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 Poincaré 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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www.doverpublications.com

About the Author:
Joseph Lehner taught at Michigan State University, the University of Maryland at College Park, and the University of Pittsburgh.

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  • PublisherDover Publications Inc.
  • Publication date2015
  • ISBN 10 0486789748
  • ISBN 13 9780486789743
  • BindingPaperback
  • Number of pages160

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9780030524707: Short Course in Automorphic Functions (Athena S.)

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ISBN 10:  0030524709 ISBN 13:  9780030524707
Publisher: Holt,Rinehart & Winston of C..., 1966
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Book Description Paperback. Condition: new. Paperback. 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 analysed. 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. Concise treatment covers basics of Fuchsian groups, development of Poincare series and automorphic forms, and the connection between theory of Riemann surfaces with theories of automorphic forms and discontinuous groups. 1966 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780486789743

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