Topics in Complex Function Theory Automorphic Functions and Abelian Integrals

Summary: AUTOMORPHIC FUNCTIONS. Fractional Linear Transformations. Noneuclidean Geometry. Discontinuous Groups. Polygon Groups. Poincar & ebreve Series. The Field of Automorphic Functions. Automorphic and Algebraic Functions. Algebraic Curves of Genus 0 and 1, Canonical Polygons. ABELIAN INTEGRALS. Reduction, Existence. The Period Matrix. The Modular Group. Canonical Transformation. The Theorem of Riemann and Roch. The Theore...m of Abel. The Jacobi Inversion Problem. Theta Functions. The Zeros of the Theta Function. Theta Quotients. Jacobi-Abel Functions. Cumulative Index: Vols. I & II [read more]