Complex Functions: An Algebraic and Geometric Viewpoint

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Gareth A. JonesCambridge University PressEdition: First Edition, 11/18/2010EAN 9780521313667, ISBN10: 052131366XPaperback, 356 pages, 22.8 x 15.2 x 2 cmLanguage: EnglishElliptic fu nctions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.Introduction1. The Riemann sphere2. Möbius transformations3. Elliptic functions4. Meromorphic continuation and Riemann surfaces5. PSL(2,R) and its discrete subgroups6. The modular groupAppendicesReferencesIndex of symbolsIndex of names and definitions. Show more