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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.

Functions of complex variables -- Congresses. --- Mathematical analysis -- Congresses. --- Functions of complex variables --- Riemann surfaces --- Topology --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Differential equations, partial. --- Partial differential equations --- Riemann surfaces. --- Topology.

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Das Buch bietet eine vollständige Darstellung der Funktionentheorie, beginnend mit der Theorie der Riemann`schen Flächen einschließlich Uniformisierungstheorie sowie einer ausführlichen Darstellung der Theorie der kompakten Riemann`schen Flächen, Riemann-Roch`schem Satz, Abel`schem Theorem und Jacobi`schem Umkehrtheorem. Hierdurch motiviert wird eine kurze Einführung in die Funktionentheorie mehrerer Veränderlicher gegeben und dann die Theorie der Abel`schen Funktionen bis hin zum Thetasatz entwickelt. Daran anschließend und hierdurch motiviert wird eine Einführung in die Theorie der höheren Modulfunktionen gegeben.

Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable.

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