The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions.
Author(s): Eberhard Freitag (auth.)
Series: Universitext
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 506
Tags: Several Complex Variables and Analytic Spaces; Functions of a Complex Variable
Front Matter....Pages i-xiii
Riemann Surfaces....Pages 1-53
Harmonic Functions on Riemann Surfaces....Pages 54-140
Uniformization....Pages 141-183
Compact Riemann Surfaces....Pages 184-299
Analytic Functions of Several Complex Variables....Pages 300-346
Abelian Functions....Pages 347-426
Modular Forms of Several Variables....Pages 427-482
Appendix: Algebraic Tools....Pages 483-493
Back Matter....Pages 494-506
